Researcher Database

EI Shin-Ichiro
Faculty of Science Mathematics Mathematics
Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

    Professor

URL

Research Interests

  • Large Area Analysis   

Research Areas

  • Mathematics / Basic analysis
  • Mathematics / General mathematics (including Probability theory/Statistical mathematics)
  • Mathematics / Global analysis

Education

  •        - 1987  Hiroshima University  Graduate School, Division of Natural Science  japan
  •        - 1982  Kyoto University  Faculty of Science  japan

Association Memberships

  • THE JAPANESE SOCIETY FOR MATHEATICAL BIOLOGY   

Research Activities

Published Papers

Books etc

  • Nonlinear dynamics in partial differential equations
    栄 伸一郎, 川島 秀一, 木村 正人(応用数学), 水町 徹 ()
    Mathematical Society of Japan 2015 9784864970228
  • A mathematical approach to research problems of science and technology : theoretical basis and developments in mathematical modeling
    西井 龍映, 栄 伸一郎, 小磯 深幸, 落合 啓之, 岡田 勘三, 斎藤 新悟, 白井 朋之 ()
    Springer 2014 9784431550594

Conference Activities & Talks

  • Motion of a pulse for mass conserved reaction-diffusion systems related to cell polarity  [Not invited]
    PDE seminar  2017/11  Chinese Academy of Science
  • Motion of a Pulse for Mass-conserved Reaction-diffusion Systems Related to Cell Polarity  [Not invited]
    2017 NCTS Workshop on Partial Differential Equations  2017/06  2017 Lecture Room B, 4F, The 3rd General Bldg., NTHU.
  • Motion of a pulse for mass conserved reaction-diffusion systems related to cell polarity  [Invited]
    EI Shin-Ichiro
    MIMS The International Conference on “Reaction-diffusion system,theory and applications"  2017/03  Meiji University (17th, 18th at Nakano Campus, 19th at Surugadai Campus)
  • Motion of pulse solution to a reaction-diffusion system with conservation of mass  [Not invited]
    EI Shin-Ichiro
    Mathematical Analysis on Nonlinear PDEs  2017/01  Tohoku University, Sendai, Japan
  • Multi-peak localized solutions for reaction-diffusion systems on two dimensional curved surface  [Invited]
    EI Shin-Ichiro
    The Second Workshop on Differential Geometry and Differential equations  2016/11  Chinese Classics Building, Renmin University of China (on the west to the Library)
  • Effect of boundaries on the motion of a spot solution in a two dimensional domain  [Not invited]
    EI Shin-Ichiro
    Reaction-Diffusion Systems in Mathematics and Biomedecine  2016/09  illa Clythia, Fr´ejus, France
  • Pulse interaction in modified FitzHugh-Nagumo equations  [Invited]
    EI Shin-Ichiro
    Mathematics of Pattern Formation  2016/09  Mathematical Research and Conference Center in B?dlewo, Poland
  • Effect of boundaries on the motion of a spot solution in a two dimensional domain  [Not invited]
    EI Shin-Ichiro
    Joint Australia-Japan workshop on dynamical systems with applications in life sciences  2016/07  Brisbane, Queensland, Australia
  • Pulse dynamics of modified FitzHugh-Nagumo equation  [Not invited]
    EI Shin-Ichiro
    2016/03
  • Pulse dynamics of modified FitzHugh-Nagumo equation  [Not invited]
    EI Shin-Ichiro
    2015 NCTS Workshop on Partial Differential Equations and Applied Mathematics  2015/12  Room B, NCTS, Tsing-Hua University, Hsinchu, Taiwan
  • Shape-dependent motion of interacting camphor  [Not invited]
    EI Shin-Ichiro
    he 16th RIES-Hokudai International Symposium  2015/11  Chateraise Gateaux Kingdom Sapporo (CGKS)
  • Interaction of asymmetric solutions in two dimensional spaces Part I, II  [Not invited]
    EI Shin-Ichiro
    2015/11
  • Pulse dynamics of modified FitzHugh-Nagumo equation  [Not invited]
    EI Shin-Ichiro
    ICMMA 2015, Self-organization, Modeling and Analysis  2015/10  Nakano Campus, Meiji University
  • Pulse dynamics of modified FitzHugh-Nagumo equation  [Not invited]
    EI Shin-Ichiro
    2015 CMC-KMRS Mathematical Biology Conference on Cross-diffusion, chemotaxis,and related problems  2015/07  KAIST (Korea Advanced Institute of Science and Technology)Daejeon, Korea
  • Weak interaction of wavefronts in FitzHugh-Nagumo systems  [Not invited]
    EI Shin-Ichiro
    2015/06
  • Motion of interacting camphors  [Not invited]
    EI Shin-Ichiro
    2015/02
  • Motion of interacting camphors  [Invited]
    EI Shin-Ichiro
    2015/01
  • Motion of interacting camphors  [Not invited]
    EI Shin-Ichiro
    2014 NCTS Applied Math. & PDE Seminar  2014/12  Lecture Room B of NCTS 4th Floor, The 3rd General Building, National Tsing Hua University, Taiwan
  • EI Shin-Ichiro
    2014/11
  • Pulse dynamics for FitzHugh-Nagumo equation on heterogeneous media  [Not invited]
    EI Shin-Ichiro
    mini-workshop on Modeling, Simulation & Analysis of Pattern Formation  2014/07  Kawai Hall, Tohoku University
  • Pulse dynamics for FitzHugh-Nagumo equation on heterogeneous media  [Not invited]
    EI Shin-Ichiro
    2014/07
  • Pulse dynamics in FitzHugh-Nagumosystems on heterogeneous media  [Not invited]
    EI Shin-Ichiro
    2014/07  Madrid, Spain, The Universidad Aut´onoma de Madrid (UAM)
  • Dynamics of localized solutions for reaction-diffusion systems in two dimensional domains  [Not invited]
    EI Shin-Ichiro
    2014/02
  • Motion of pulses for FitzHugh-Nagumo equation on heterogeneous media  [Not invited]
    EI Shin-Ichiro
    2014/01
  • Dynamics of pulses for FHN on heterogeneous media  [Not invited]
    EI Shin-Ichiro
    2013/11
  • Dynamics of Localized Solutions for Reaction-Diffusion Systems on Curved Surface  [Not invited]
    EI Shin-Ichiro
    2013/10  KAIST(Korea Advanced Institute of Science and Technology Daejeon, Korea
  • Dynamics of Localized patterns for Reaction-Diffusion Systems on a Curved Surface  [Not invited]
    EI Shin-Ichiro
    Workshop on Mathematical Modelling and Analysis in the Life Sciences  2013/06  Carry-le-Rouet, France
  • Dynamics of Localized Solutions for Reactiondiffusion Systems on Curved Surface  [Not invited]
    EI Shin-Ichiro
    IMA Special Workshop Joint US-Japan Conference for Young Researchers on Interactions among Localized Patterns in Dissipative Systems  2013/06  IMA Keller Hall 3-180
  • Renormalization-Group approach to the movement of interacting pulses  [Not invited]
    EI Shin-Ichiro
    2012/09
  • Dynamics of localized solutions for reaction-diffusion systems on two dimensional domain,Nonlinear Partial Differential Equations,Dynamical Systems and Their Applications{in honor of Professor Hiroshi Matano on the occasion of his 60th birthday  [Not invited]
    EI Shin-Ichiro
    2012/09  Room 420, Research Institute for Mathematical Sciences, Kyoto University
  • Dynamics of localized solutions for reaction-diffusion systems in two-dimensional domains  [Not invited]
    EI Shin-Ichiro
    Turing Symposium on Morphogenesis--Mathematical Approaches Sixty Years after Alan Turing  2012/08
  • Infinite dimensional relaxation oscillation in a two mode randomly walking model with growth  [Not invited]
    EI Shin-Ichiro
    2011/11
  • Infinite dimensional relaxation oscillation  [Not invited]
    EI Shin-Ichiro
    LOCALIZED MULTI-DIMENSIONAL PATTERNS IN DISSIPATIVESYSTEMS: THEORY, MODELING, AND EXPERIMENTS  2011/07  BIRS, Banff, Canada
  • Dynamics of pulses in two dimensional thin domain  [Not invited]
    EI Shin-Ichiro
    The 3rd Kyushu University-POSTECH Joint Workshop- Partial Differential Equations and Fluid Dynamics  2011/06  POSTEC, Korea
  • Dynamics of pulses in two dimensional thin domain  [Not invited]
    EI Shin-Ichiro
    Far-From-Equilibrium Dynamics  2011/01
  • Dynamics of pulses in two dimensional thin domains  [Not invited]
    EI Shin-Ichiro
    2010/11
  • The effect of boundary conditions to the pulse dynamics  [Not invited]
    EI Shin-Ichiro
    2010/02
  • The effect of boundary conditions to the dynamics of pulse solutions for reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2009/12
  • Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2009/12
  • The effect of boundary conditions to the pulse dynamics  [Not invited]
    EI Shin-Ichiro
    2009/09
  • The effect of boundary conditions to the dynamics of pulse solutions for reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2009/08
  • The dynamics of boundary spikes for reaction-diffusion systems in 2D  [Not invited]
    EI Shin-Ichiro
    2nd International conference on Reaction-diffusion systems and viscosity solutions  2009/07  Department of applied mathematics, Providence University, Taiwan
  • The effect of boundary conditions to the pulse dynamics  [Not invited]
    EI Shin-Ichiro
    Reaction-Diffusion Systems: Modeling and Analysis  2009/06  ReaDiLab Conference in Orsay (France)
  • Dynamics of boundary spikes for Gierer-Meinhardt model in 2D  [Not invited]
    EI Shin-Ichiro
    Verified Computation of Solutions for Partial Differential Equations and Related Topics  2009/05  The Hong Kong Polytechnic University
  • Interaction of deformed pulses in two dimensional spaces  [Not invited]
    EI Shin-Ichiro
    2008/12
  • Motion of a transition layer in heterogeneous environment  [Not invited]
    EI Shin-Ichiro
    2008/11
  • The motion of a transition layer for a bistable reaction diffusion equation in one dimensional space with heterogeneous environment,Mathematical Understanding of Complex Systems arising in Biology and Medicine  [Not invited]
    EI Shin-Ichiro
    CNRS Japan-France LIA ReaDiLab  2008/08
  • Dynamics of Pulses Constructed by Front Interaction  [Not invited]
    EI Shin-Ichiro
    2008/08
  • The dynamics of spikes along boundaries in two dimensional space  [Not invited]
    EI Shin-Ichiro
    2008/03
  • Boundary spikes for reaction-diffusion systems II  [Not invited]
    EI Shin-Ichiro
    2007/11
  • The dynamics of boundary spikes for reaction-diffusion systems in space dimension 2  [Not invited]
    EI Shin-Ichiro
    Mathematical modeling and analysis in biological and chemical systems  2007/09  ReaDiLab Conference in Orsay & IHES (France)
  • Interface Equations for Reaction-Diffusion Systems Near Critical Point  [Not invited]
    EI Shin-Ichiro
    2007/05  Snowbird
  • On the validity of mean curvature flow for weakly curved interfaces in reaction-diffusion systems with balanced bistable nonlinearity  [Not invited]
    EI Shin-Ichiro
    2007/01
  • Dynamics of Pulses Constructed by Front Interaction  [Not invited]
    EI Shin-Ichiro
    Internal conference on RD and Viscosity solutions  2007/01
  • Interface Equations for Reaction-Diffusion Systems Near Critical Point  [Not invited]
    EI Shin-Ichiro
    Workshop on Reaction-Diffusion: Theory & Applications  2006/12  Lecture Room: M210, Math Building, NTNU (Ting Chou Road’s Campus)
  • Front dynamics in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2006/10
  • Dynamics of front solutions in heterogeneous media  [Not invited]
    EI Shin-Ichiro
    the Conference "Dynamics of nonlinear waves"  2006/04  Groningen University, Groningen
  • The dynamics of boundary spikes for reaction-diffusion systems in space dimension 2  [Not invited]
    EI Shin-Ichiro
    2006/01
  • Dynamics of front solutions in heterogeneous media  [Not invited]
    EI Shin-Ichiro
    2005/12
  • Dynamics of front solutions of reaction-diffusion systems with bistable nonlinearity  [Not invited]
    EI Shin-Ichiro
    2005/10
  • The motion of fronts in heterogeneous reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2005/08  Providence University, Taiwan
  • A Variational Approach to Singular Perturbation Problems  [Not invited]
    EI Shin-Ichiro
    2005/08
  • Interacting pulses in reaction diffusion systems  [Not invited]
    EI Shin-Ichiro
    2005/08
  • Dynamics of Turing patterns for reaction-diffusion systems in a cylindrical domain on 2D  [Not invited]
    EI Shin-Ichiro
    2005/08  Feng Chia University,Taiwan
  • Dynamics of spiral solutions for reaction-diffusion systems with bistable nonlinearity  [Not invited]
    EI Shin-Ichiro
    2005/07
  • A variational approach to singular perturbation problems  [Not invited]
    EI Shin-Ichiro
    2004/11
  • Dynamics of pulse solutions in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2004/11
  • Dynamics of patterns in reaction-diffusion systems on two dimensions  [Not invited]
    EI Shin-Ichiro
    Nonlinear PDE symposium  2004/11
  • A variational approach to singular perturbation problems  [Not invited]
    EI Shin-Ichiro
    2004/11  台湾 清宣大学応用数学教室
  • Dynamics of Turing patterns for reaction-diffusion systems in a cylindrical domain on 2D  [Not invited]
    EI Shin-Ichiro
    「Hyperbolic problems, Theory, Numerics, Applications」  2004/09
  • Dynamics of Turing patterns in cylindrical domains on 2D  [Not invited]
    EI Shin-Ichiro
    2004/07
  • Dynamics of Turing patterns in cylindrical domains on 2D  [Not invited]
    EI Shin-Ichiro
    NCTS 2004 Workshop on Reaction-Diffusion Equations and Related Topics  2004/05  Lecture Room A of NCTS, 4th Floor, The 3rd General Building National Tsing Hua University, Hsinchu.Taiwan
  • Dynamics of Turing Patterns for Reaction-Diffusion Systems in a Cylindrical Domain in 2D  [Not invited]
    EI Shin-Ichiro
    Mathematical Understanding of Invasion Processes in Life Sciences  2004/03  CIRM, Luminy, France
  • 2次元帯状領域におけるTuringパターン  [Not invited]
    EI Shin-Ichiro
    Hakozaki Workshop on Applied and Numerical Analysis  2004/01
  • The dynamics of patterns for reaction-diffusion systems in a cylindrical domain in 2D  [Not invited]
    EI Shin-Ichiro
    2003/10
  • The dynamics of patterns for reaction-diffusion systems in a cylindrical domain in 2D  [Not invited]
    EI Shin-Ichiro
    BIRS Workshops: Defects and their Dynamics and Localization Behavior in Reaction-Diffusion Systems and Applications to the Natural Sciences  2003/08  Banff Center Banff Canada
  • 元シリンダー領域におけるパターンの運動について  [Not invited]
    EI Shin-Ichiro
    Hiroshima Mathematical Analysis Seminar No.60  2003/06
  • A new type of the Billiard problem arising from reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Workshop on Dynamics of Nonlinear waves  2003/01  Oberwolfach, Germany
  • Dynamics of patterns in reaction-diffusion systems and the related topics  [Not invited]
    EI Shin-Ichiro
    2002/11
  • Dynamics of Pulses in Reaction-Diffusion Systems  [Not invited]
    EI Shin-Ichiro
    Development of numerical nethods for dynamics of interfaces and its applications to experiments in science and Engineering II  2002/07
  • Pulse dynamics near a critical point in reaciton-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Workshop on "Singular limit analysis of reaciton-diffusion systems  2002/07  L'Aquila Univ. L'Aquila Italy
  • Dynamics of pulses in reaciton-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2002/06
  • Dynamics of pulse-like localized pattern in higher dimension  [Not invited]
    EI Shin-Ichiro
    Traveling waves: Theory and Applications  2001/10
  • Pulse dynamics approach to the analysis on the self-replicating behavior  [Not invited]
    EI Shin-Ichiro
    Patterns and Waves - Mathematics and NonlinearChemistry  2001/08  Lorentz Center Leiden
  • Invariant manifold and its application to the pulse dynamics  [Not invited]
    EI Shin-Ichiro
    Workshop on "Asymptotics and Dynamics in Nonlinear Diffusive Systems  2001/06
  • Dynamics of pulses in reaction-diffusion systems,Singular limits of reaction-diffusion systems: Interfaces and spikes  [Not invited]
    EI Shin-Ichiro
    2001/03  Lorentz Center, Leiden, Holland
  • Minisynposium on nonlinear dynamics and dissipative systems  [Not invited]
    EI Shin-Ichiro
    2001/02
  • Dyanamics of pulse solutions in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2000/12
  • Dynamics of localized solutions in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    The first east Asia Symposium on Nonlinear PDE  2000/09
  • Dynamics of interacting pulses in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Organized session "Pulse dynamics in dissipative systems"  2000/08  Pacific RIM dynamical systems conference, Maui Marriott Resort
  • Pulse dynamics of reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    2000/05
  • Pulse dynamics approach to self-replicating patterns  [Not invited]
    EI Shin-Ichiro
    2000/05
  • The dynamics of pulses on reaction-diffusion systems II  [Not invited]
    EI Shin-Ichiro
    NCTS Seminar  2000/05
  • Dynamics of pulses for reaction-diffusion systems in higher dimensional space  [Not invited]
    EI Shin-Ichiro
    2000/05  台湾国立交通大学(NCTU) Science Building I Room 223
  • The dynamics of pulses on reaction-diffusion systems I  [Not invited]
    EI Shin-Ichiro
    NCTS Seminar  2000/05
  • Dynamics of pulses for reaction-diffusion systems in higher dimensional space  [Not invited]
    EI Shin-Ichiro
    2000/05
  • The dynamics of interfaces in the scalar reaction-diffusion equations I&II  [Not invited]
    EI Shin-Ichiro
    NCTS Seminar  2000/04
  • Dynamics of interacting pulses in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Equations aux Derivees Partielles Non Lineaires Frontieres libres,Interfaces et Singularites  2000/03
  • Pulse interaction and its application to bifurcation problems  [Not invited]
    EI Shin-Ichiro
    2000/02
  • The dynamics of spike solutions for reaction-diffusion systems in two dimensional space  [Not invited]
    EI Shin-Ichiro
    IMS Workshop on Reaction-Diffusion Systems  1999/12  The Chinese University of Hong Kong
  • Renormalization-group Method for Reduction of Evolution Equations  [Not invited]
    EI Shin-Ichiro
    1999/07
  • Pulse-interaction approach to self-replicating dynamics in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    1999/07
  • Dynamics of Metastable Localized Patterns and its Application to the Interaction of Spike Solutions for The Gierer-Meinhardt System in 2 dimensinal space  [Not invited]
    EI Shin-Ichiro
    1999/07
  • Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes  [Not invited]
    EI Shin-Ichiro
    1999/06  Anogia Academic village, Crete
  • On the dynamics of spike solutions in pattern formation model equations on 2 dimensional domains  [Not invited]
    EI Shin-Ichiro
    1999/05
  • Pulse-interaction approach to self-replicating dynamics in reaction-diffusion sytems  [Not invited]
    EI Shin-Ichiro
    Differential Equations Seminar  1999/03  The University of Tennessee Ayres Hall ROOM 214
  • Pulse-dynamics approach to self-replicating patterns  [Not invited]
    EI Shin-Ichiro
    Special NSC Seminar on Nonlinear Dynamic  1999/01
  • The motion of weakly interacting pulses in reaction-diffusion systems - from the self-replicating phenomena point of view  [Not invited]
    EI Shin-Ichiro
    Recent Topics in Nonlinear PD  1999/01
  • Motion of weakly interacting pulses in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Reaction-Diffusion Systems:Theories and Applications  1998/12
  • The motion of weakly interacting pulses in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    PDE seminar  1998/10  Department of Mathematics The Chinese University of Hong Kong, Room 222B, Lady Shaw Building
  • The dynamics of pulses in reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Workshop on Nonlinear Partial Diffusion Equations and Related Topics, Ryukoku '98  1998/06
  • A three partition problem arising from competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    First Pacific RIM Conference on Mathematics  1998/01  Applied PDE session, City University of Hong Kong, Hong Kong
  • A three partition problem arising from competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Workshop on Singularities Arising in Nonlinear Problems  1997/11
  • A three partition problem arising from competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    Internatinal Conference on Asymtotics in Nonlinear Diffusion Systems  1997/07
  • A three partition problem arising from competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    1997/06
  • A three partition problem arising from competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    1997/05
  • The Equation of Motion for Interacting Pulses  [Not invited]
    EI Shin-Ichiro
    SFU's Applied Mathematics Seminar  1996/11  Room K9509, SFU CAMPUS
  • Equations of Motions for Interacting Pulses  [Not invited]
    EI Shin-Ichiro
    Applied Mathematics Colloquium  1996/09  Old Computer Science Building Room 301, Institute of Applied Mathematics,UBC
  • Slow dynamics of interfaces intersecting the boundary in a strip-like domain  [Not invited]
    EI Shin-Ichiro
    1996/01
  • Equation of motion for interacting pulses  [Not invited]
    EI Shin-Ichiro
    1994/10
  • ソリトン間の相互作用とphase dynamics  [Not invited]
    EI Shin-Ichiro
    1994/04
  • Stability of stationary interfaces with contact angle in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    1994/02
  • Stability of stationary interfaces with contact angle in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    1994/01
  • Stability of stationary interfaces with boundaries in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    1994/01
  • Stability of stationary interfaces in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    JAMI SEMINAR -FALL 1993  1993/11  Department of Mathematics Johns Hopkins University (USA)
  • Dynamics of interfaces in competition-diffusion systems  [Not invited]
    EI Shin-Ichiro
    1993/09
  • The stability of stationary interfaces in generalized mean curvature flow with boundaries  [Not invited]
    EI Shin-Ichiro
    1993/09
  • Stability of stationary interfaces in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    1993/05
  • Stability of stationary interfaces with boundaries in a generalized mean curvature flow  [Not invited]
    EI Shin-Ichiro
    1994/01
  • Dynamics of interfaces of reaction-diffusion equations in inhomogeneous media  [Not invited]
    EI Shin-Ichiro
    Workshop on Dynamical Systems,Theory and its Applications  1992/11
  • Dynamics of interfaces of reaction-diffusion equations in inhomogeneous media  [Not invited]
    EI Shin-Ichiro
    1992/10
  • Interfacial dynamics arising from some reaction-diffusion equations  [Not invited]
    EI Shin-Ichiro
    1992/06
  • Interfacial dynamics arising from some reaction-diffusion equations  [Not invited]
    EI Shin-Ichiro
    1992/06
  • Effect of Domain-shape on Combustion Processes  [Not invited]
    EI Shin-Ichiro
    1991/06
  • Oscillations in Chemotaxis Model  [Not invited]
    EI Shin-Ichiro
    1991/03
  • Effect of Domain-shape on Combustion Processes  [Not invited]
    EI Shin-Ichiro
    1991/01
  • On fast and slow motions in reaction diffusion systems  [Not invited]
    EI Shin-Ichiro
    1990/07
  • Relaxation-oscillation in infinite dimensional dynamical systems  [Not invited]
    EI Shin-Ichiro
    Nonlinear Analysis Semina  1989/11
  • Relaxation-Oscillations in Infinite Dimensional Dynamical Systems  [Not invited]
    EI Shin-Ichiro
    1989/10
  • On fast and slow motions in reaction-diffusion systems with an application to relaxation oscillations  [Not invited]
    EI Shin-Ichiro
    1989/10
  • Reduction of Certain Quasi-linear Parabolic Equations to Finite Dimensional Flows  [Not invited]
    EI Shin-Ichiro
    1989/06
  • Two-timing methods with applications to nonlinear parabolic equations  [Not invited]
    EI Shin-Ichiro
    1989/01
  • The effect of non-local convection on reaction-diffusion equations  [Not invited]
    EI Shin-Ichiro
    1988/06  Heriot-Watt University (U.K.)
  • On two-timing methods in abstract parabolic equations with applications to reaction-diffusion systems,in Conferenceon reaction diffusion equations  [Not invited]
    EI Shin-Ichiro
    1988/05  Heriot-Watt University(U.K.)
  • Two-timing methods とその力学系への応用  [Not invited]
    EI Shin-Ichiro
    1988/01
  • Two-timing methods with applications to dynamical systems  [Not invited]
    EI Shin-Ichiro
    1987/11
  • Two-timing methods with applications to heterogeneous reaction-diffusion systems  [Not invited]
    EI Shin-Ichiro
    1987/10
  • Two-timing methods with applications to bifurcation problems  [Not invited]
    EI Shin-Ichiro
    Work shop of finite and infinite dynamical system  1987/09
  • A spatially aggregating population model involving size-distributed dynamics  [Not invited]
    EI Shin-Ichiro
    1987/04
  • Transient and large time behaviors to heterogeneous reaction-diffusion equations  [Not invited]
    EI Shin-Ichiro
    1987/02

MISC

  • Chao Nien Chen, Shin Ichiro Ei, Shin Ichiro Ei, Shyuh yaur Tzeng  Physica D: Nonlinear Phenomena  2018/01   [Not refereed] [Not invited]  
    © 2018 Elsevier B.V. Particle like structures have been observed in many fields of science. In a homogeneous medium, a stable, standing pulse is a localized wave that may arise when nonlinear and dissipative effects are in balance. In this paper, we investigate certain phenomena associated with the dynamics of pulse solutions for a FitzHugh–Nagumo reaction–diffusion model. When two pulses are located far from one another initially, their weak interaction drives the subsequent slow dynamics. Our comprehension of the standing pulse profiles allows us to quantitatively characterize their interplay; when the diffusivity of the activator is small compared to that of the inhibitor, the two pulses repel. In addition, using a center-manifold reduction to study the presence of heterogeneities in the environment, we demonstrate that the pulses will move so as to maximize the strength of activation or minimize that of inhibition. The pulse motion will also be influenced by the reaction mechanism.
  • 田中吉太郎, 八杉徹雄, 佐藤純, 栄伸一郎  日本応用数理学会年会講演予稿集(CD-ROM)  2017-  43‐44  2017/09   [Not refereed] [Not invited]
  • 田中吉太郎, 八杉徹雄, 佐藤純, 長山雅晴, 栄伸一郎  計算工学講演会論文集(CD-ROM)  22-  ROMBUNNO.D‐05‐5  2017/05   [Not refereed] [Not invited]
  • 田中 吉太郎, 八杉 徹雄, 佐藤 純, 長山 雅晴, 栄 伸一郎  計算工学講演会論文集 Proceedings of the Conference on Computational Engineering and Science  22-  2017/05   [Not refereed] [Not invited]
  • 栄伸一郎  白石記念講座  67th-  29  -42  2015/11   [Not refereed] [Not invited]
  • 栄伸一郎  電子情報通信学会誌  98-  (11)  961  -966  2015/11   [Not refereed] [Not invited]
  • 栄 伸一郎  電子情報通信学会誌 = The journal of the Institute of Electronics, Information and Communication Engineers  98-  (11)  961  -966  2015/11   [Not refereed] [Not invited]
  • Ei Shin-Ichiro  応用数理  24-  (1)  34  -36  2014/03   [Not refereed] [Not invited]
  • 栄伸一郎  応用数理  24-  (1)  34  -36  2014/03   [Not refereed] [Not invited]
  • 栄 伸一郎  応用数理  24-  (1)  34  -36  2014/03   [Not refereed] [Not invited]
  • EI Shin-Ichiro, IZUHARA Hirofumi, MIMURA Masayasu  RIMS Kokyuroku Bessatsu  35-  31  -40  2012/12   [Not refereed] [Not invited]
  • Weng Wulin, Ei Shin-Ichiro, Ohgane Kunishige, Ogane Kunishige  Journal of Math-for-Industry (JMI)  4-  (0)  123  -133  2012/10   [Not refereed] [Not invited]  
    Based on neurophysiological studies, a walking model has been proposed, which is the coupling of two oscillatory systems, i.e., a central pattern generator (CPG) and a musculoskeletal system (Body). The walking model can well reproduce human walking. However, time delays on a sensorimotor loop give a serious problem in motor control in general. Indeed even a short time delay induces the walking model to fall. Theoretical studies have shown that the eng=walking model can overcome the time delays by the flexible-phase locking. It emerges from the following two conditions; 1) activity of CPG and Body has stability of limit cycle; 2) a sign differs between coupling coefficients of the connection from Body to CPG and from CPG to Body, i.e., the afferent and efferent connection. Physical or physiological interpretation of this two theoretical conditions is an important problem. The condition 1) has already interpreted [1]. In this paper, we gain a physical interpretation of the condition 2). We introduce the simplified model fit to best analyze. Analyzing the simplified model, this study leads to the interpretation in which signs of the coupling coefficients corresponding to the excitatory and inhibitory connection are regarded as a force to forward and backward shift the CPG activity, respectively. This is an essential element to yield the flexible-phase locking.
  • EI SHIN-ICHIRO  RIMS Kokyuroku Bessatsu  31-  195  -210  2012/05   [Not refereed] [Not invited]
  • Weng Wulin, Ei Shin-Ichiro, Ohgane Kunishige  JMI : journal of math-for-industry  4-  123  -133  2012   [Not refereed] [Not invited]
  • Ei Shin-Ichiro, Ohgane Kunishige, 栄 伸一郎, 大金 邦成  Kyushu Journal of Mathematics  65-  (2)  197  -217  2011/09   [Not refereed] [Not invited]  
    We develop a systematic method for deriving the phase dynamics of perturbed periodic solutions. The method is to regard periodic solutions as slowly modulated traveling solutions on the circle. There, problems are reduced to the perturbed problems from stationary solutions on the circle. This makes the treatment of periodic solutions far easier and systematic. We also give the rigorous proofs for this method.
  • Ei Shin-Ichiro, Nishiura Yasumasa, Ueda Kei-Ichi  JMI  1-  91  -95  2009   [Not refereed] [Not invited]  
    The dynamics of a pulse for reaction-diffusion systems in 1D is considered in the neighborhood of the bifurcation point with codimension two, at which both of saddle-node and drift bifurcations occur at the same time. It is theoretically shown that when the bifurcation parameter is close to such a bifurcation point, a pulse moves with oscillation, and then starts to split.
  • Ei Shin-Ichiro, Tsujikawa Tohru  RIMS Kokyuroku  1588-  118  -123  2008/04   [Not refereed] [Not invited]
  • 栄伸一郎  日本物理学会講演概要集  63-  (1)  302  2008/02   [Not refereed] [Not invited]
  • Ei Shin-Ichiro  Meeting abstracts of the Physical Society of Japan  63-  (1)  2008/02   [Not refereed] [Not invited]
  • EI Shin-Ichiro, IKEDA Hideo, KAWANA Takeyuki  Japan journal of industrial and applied mathematics  25-  (1)  117  -147  2008/02   [Not refereed] [Not invited]
  • Shin Ichiro Ei, Hideo Ikeda, Takeyuki Kawana  Japan Journal of Industrial and Applied Mathematics  25-  117  -147  2008/01   [Not refereed] [Not invited]  
    In this paper, two component reaction-diffusion systems with a specific bistable nonlinearity are concerned. The systems have the bifurcation structure of pitch-fork type of traveling front solutions with opposite velocities, which is rigorously proved and the ordinary differential equations describing the dynamics of such traveling front solutions are also derived explicitly. It enables us to know rigorously precise information on the dynamics of traveling front solutions. As an application of this result, the imperfection structure under small perturbations and the dynamics of traveling front solutions on heterogeneous media are discussed.
  • OHGANE Kunishige, EI Shin-ichiro  RIMS Kokyuroku Bessatsu  3-  207  -230  2007/11   [Not refereed] [Not invited]
  • S. I. Ei, M. Mimura, M. Nagayama  Discrete and Continuous Dynamical Systems  14-  31  -62  2006/01   [Not refereed] [Not invited]  
    This paper is concerned with the dynamics of travelling spot solutions in two dimensions. Travelling spot solutions are constructed under the bifurcation structure with Jordan block type degeneracy. It is shown that if the velocity is very slow, such travelling spots possess reflection property. In order to do it, we derive the reduced ordinary differential equations describing the dynamics of interacting travelling spots in RD systems by using center manifold theory. This reduction enables us to prove that two very slowly travelling spots reflect before collision as if they were elastic particles.
  • OHGANE Kunishige, OHGANE Akane, MAHARA Hitoshi, EI Shin-ichiro  形の科学会誌 = Bulletin of the Society for Science on Form  20-  (2)  169  -170  2005/11   [Not refereed] [Not invited]
  • Shin Ichiro Ei, Masataka Kuwamura, Yoshihisa Morita  Physica D: Nonlinear Phenomena  207-  171  -219  2005/08   [Not refereed] [Not invited]  
    In this paper singular perturbation problems in reaction-diffusion systems are studied from a viewpoint of variational principle. The goal of the study is to provide an unified and transparent framework to understand existence, stability and dynamics of solutions with transition layers in contrast to previous works in many literatures on singular perturbation theory. © 2005 Elsevier B.V. All rights reserved.
  • Ei Shin-Ichiro  RIMS Kokyuroku  1425-  122  -129  2005/04   [Not refereed] [Not invited]
  • Ei Shin-ichiro  Bulletin of the Japan Society for Industrial and applied Mathematics  14-  (1)  35  -47  2004/03   [Not refereed] [Not invited]
  • 栄 伸一郎  数理解析研究所講究録  1356-  108  -115  2004/02   [Not refereed] [Not invited]
  • EI Shin-ichiro  盛岡応用数学小研究集会報告集  2003-  5  -10  2004/01   [Not refereed] [Not invited]  
    Reaction-dffusion systems in an infinitely long strip-like domain with finite width in 2D are treated.We construct the solution connecting different types of stationary solutions at infinity by considering the neighborhood of Turing instability.We also derive 4th order equations of buckling type which shows the dynamics of the connecting solutions.
  • 栄 伸一郎  数理解析研究所講究録  1313-  149  -158  2003/04   [Not refereed] [Not invited]
  • 栄伸一郎  横浜市立大学論叢 自然科学系列  53-  (3)  119  -134  2002/10   [Not refereed] [Not invited]
  • EI Shin-Ichiro, WEI Juncheng  Jpn. J. Indust. Appl. Math.  19-  (2)  181  -226  2002/06   [Not refereed] [Not invited]
  • S. I. Ei, M. Mimura, M. Nagayama  Physica D: Nonlinear Phenomena  165-  176  -198  2002/05   [Not refereed] [Not invited]  
    It had been long believed that one-dimensional travelling pulses and the corresponding two-dimensional expanding rings and spiral waves arising in excitable reaction-diffusion systems annihilate when they closely approach one another. However, recently it has been numerically confirmed that if the velocity is very slow, expanding rings and spiral do not necessarily annihilate. In particular, in some situation, two closely approaching pulses reflect, as if they were elastic like objects. By using the center manifold theory, we show that if there are travelling pulses which primarily and super-critically bifurcate from a standing pulse when some parameter is varied, they possess reflection mechanism if the velocity is very slow. © 2002 Elsevier Science B.V. All rights reserved.
  • Shin Ichiro Ei, Juncheng Wei  Japan Journal of Industrial and Applied Mathematics  19-  181  -226  2002/01   [Not refereed] [Not invited]  
    In this paper, the Gierer-Meinhardt model systems with finite diffusion constants in the whole space R2is considered. We give a regorous proof on the existence and the stability of a single spike solution, and by using such informations, the repulsive dynamics of the interacting multi single-spike solutions is also shown when distances between spike solutions are sufficiently large. This clarifies some part of the mechanism of the evolutional process of localized patterns appearing in the Gierer-Meinhardt model equations.
  • Shin Ichiro Ei  Journal of Dynamics and Differential Equations  14-  85  -137  2002/01   [Not refereed] [Not invited]  
    The interaction of stable pulse solutions on R1is considered when distances between pulses are sufficiently large. We construct an attractive local invariant manifold giving the dynamics of interacting pulses in a mathematically rigorous way. The equations describing the flow on the manifold is also given in an explicit form. By it, we can easily analyze the movement of pulses such as repulsiveness, attractivity and/or the existence of bound states of pulses. Interaction of front solutions are also treated in a similar way. © 2002 Plenum Publishing Corporation.
  • EI Shin-ichiro, NISHIURA Yasumasa, UEDA Kei-ichi  Japan J. Indust. Appl. Math.  18-  (2)  181  -205  2001/06   [Not refereed] [Not invited]
  • Shin Ichiro Ei, Yasumasa Nishiura, Yasumasa Nishiura, Kei Ichi Ueda  Japan Journal of Industrial and Applied Mathematics  18-  181  -205  2001/01   [Not refereed] [Not invited]  
    Since early 90's, much attention has been paid to dynamic dissipative patterns in laboratories, especially, self-replicating pattern (SRP) is one of the most exotic phenomena. Employing model system such as the Gray-Scott model, it is confirmed also by numerics that SRP can be obtained via destabilization of standing or traveling spots. SRP is a typical example of transient dynamics, and hence it is not a priori clear that what kind of mathematical framework is appropriate to describe the dynamics. A framework in this direction is proposed by Nishiura-Ueyama [16], i.e., hierarchy structure of saddle-node points, which gives a basis for rigorous analysis. One of the interesting observation is that when there occurs self-replication, then only spots (or pulses) located at the boundary (or edge) are able to split. Internal ones do not duplicate at all. For 1D-case, this means that the number of newly born pulses increases like 2k after k-th splitting, not 2n-splitting where all pulses split simultaneously. The main objective in this article is two-fold: One is to construct a local invariant manifold near the onset of self-replication, and derive the nonlinear ODE on it. The other is to study the manner of splitting by analysing the resulting ODE, and answer the question "2n-splitting or edge-splitting?" starting from a single pulse. It turns out that only the edge-splitting occurs, which seems a natural consequence from a physical point of view, because the pulses at edge are easier to access fresh chemical resources than internal ones.
  • Ei Shin-Ichiro  RIMS Kokyuroku  1178-  87  -94  2000/12   [Not refereed] [Not invited]
  • Shin Ichiro Ei, Kazuyuki Fujii, Teiji Kunihiro  Annals of Physics  280-  236  -298  2000/03   [Not refereed] [Not invited]  
    The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t0=t is naturally understood where t0is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation is semi-simple, i.e., diagonalizable; when A is not semi-simple and has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink-anti-kink and soliton-soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears. © 2000 Academic Press.
  • Shin Ichiro Ei, Ryo Ikota, Masayasu Mimura  Interfaces and Free Boundaries  1-  57  -80  1999/01   [Not refereed] [Not invited]  
    © Oxford University Press 1999. We consider a reaction-diffusion system to describe the interaction of three competing species which move by diffusion in R2, under the situation where all of the diffusion rates are small and all of the inter-specific competition rates are large. The resulting system possesses three locally stable spatially constant equilibria, each of which implies that only one of the competing species survive and the other two are extinct. Since the diffusion rates are small, internal layer regions appear as sharp interfaces with triple junctions, which generally divide the whole plane into three different regions occupied by only one of the species. The dynamics of interfaces as well as triple junctions are numerically studied. More specifically, assuming that three competing species are almost equal in competitive strength, we derive an angle condition between any neighboring interfaces at triple junctions by formal asymptotic analysis. Furthermore, for more general cases, we numerically study the dynamics of segregating patterns of three competing species from interfacial view points.
  • Ei Shin-Ichiro, Eiji Yanagida  SIAM Journal on Mathematical Analysis  29-  555  -595  1998/05   [Not refereed] [Not invited]  
    The dynamics of interfaces in the Allen-Cahn equation is studied. If a domain in R2 has constant width along a smooth curve, it is called a strip-like domain. We derive an equation which describes the motion of a straight interface intersecting the boundary of the strip-like domain. The equation shows that the motion is slower than the mean curvature flow, but faster than the very slow dynamics.
  • EI SHIN'ICHIRO  数理科学  35-  (11)  23  -29  1997/11   [Not refereed] [Not invited]
  • EI Shin-Ichiro, IIDA Masato, YANAGIDA Eiji  Japan journal of industrial and applied mathematics  14-  (1)  1  -23  1997/02   [Not refereed] [Not invited]
  • Shin Ichiro Ei, Masato Iida, Eiji Yanagida  Japan Journal of Industrial and Applied Mathematics  14-  1  -23  1997/01   [Not refereed] [Not invited]  
    Consider the equation ut= ε2div(D(x)∇u) + f(u;ε) in ℝn, where D(x) is a positive function of x ∈ ℝn, f is the derivative of a bistable potential, and ε > 0 is a small parameter. Let Γ(T), T ∈ [0,T0], be a one-parameter family of smooth hypersurfaces which move with the time scale T = ε2t according to a certain generalized mean curvature flow. It is shown that, if the initial data have an interface which is close to Γ(0), then the interface remains close to Γ(ε2t) for t ε [0,T0/ε2]. Moreover, if T0= ∞ and Γ(T) converges to a stable stationary hypersurface as T → ∞, then the interface remains close to Γ(ε2t) for all t ≥ 0.
  • S. I. Ei, M. H. Sato, E. Yanagida  American J. Math.  118-  (3)  653  -687  1996/06   [Not refereed] [Not invited]  
    The dynamics of a moving hypersurface in a domain D C ℝN is studied. It is assumed that the hypersurface moves depending on its curvature, normal vector and position with the boundary that intersects ∂D with a constant contact angle. A stability criterion about a stationary hypersurface is established in the form of an eigenvalue problem, which includes geometrical information of ∂D and the stationary hypersurface.
  • Shin Ichiro Ei, Eiji Yanagida  Journal of Dynamics and Differential Equations  7-  423  -435  1995/07   [Not refereed] [Not invited]  
    A study is made for equations of evolving curves on a two-dimensional square domain Ω. It is assumed that a curve moves depending on its curvature, normal vector, and position and is orthogonal to ∂Ω at its end points. Under some conditions, instability of stationary solutions is proved through an eigenvalue analysis. © 1995 Plenum Publishing Corporation.
  • EI SHIN'ICHIRO  横浜市立大学論叢 自然科学系列  46-  (2)  45  -64  1995/03   [Not refereed] [Not invited]
  • Ei Shin-Ichiro, Ohta Takao  Bussei Kenkyu  63-  (5)  628  -634  1995/02   [Not refereed] [Not invited]  
    この論文は国立情報学研究所の電子図書館事業により電子化されました。
  • EI S‐I, YANAGIDA E  SIAM J. Appl. Math.  54-  (5)  1355  -1373  1994/01   [Not refereed] [Not invited]  
    This paper is concerned with the dynamics of interfaces in the Lotka-Volterra competition-diffusion system ut= ε2Δu+u(1-u-cw), wt= ε2DΔw+w(a-bu-w), in Rn, where ε>0 is a small parameter and D>0 is a constant. If 0<1/c0 is a weighted mean of 1 and D, and κ is the mean curvature of the interface.
  • EI S‐I, OHTA T  Physical Review E  50-  (6)  4672  -4678  1994/01   [Not refereed] [Not invited]  
    We develop a systematic method of deriving the equation of motion for interacting fronts or pulses in one dimension. The theory is applicable to both dissipative and dispersive systems. In the case of the time-dependent Ginzburg-Landau equation, which is a typical example of a dissipative system, the front equation obtained is the same as has been obtained previously. The pulse interaction is also derived for the Kortewegde Vries equation, emphasizing the difference between the cases with and without dissipative terms. © 1994 The American Physical Society.
  • SAKAE SHIN'ICHIRO  応用数学合同研究集会報告集 平成6年  59.1-59.2  1994   [Not refereed] [Not invited]
  • Ei Shin-Ichiro, Yanagida Eiji  Journal of The Faculty of Science, The University of Tokyo, Section IA, Mathematics  40-  (3)  651  -661  1993   [Not refereed] [Not invited]
  • M. Kuwamura, S. I. Ei, M. Mimura  Japan Journal of Industrial and Applied Mathematics  9-  35  -77  1992/02   [Not refereed] [Not invited]  
    We consider a bistable reaction-diffusion equation coupled with a time-dependent constrained condition {Mathematical expression} where γ, δ and ε are positive constants. This equation lies in a framework of activator-inhibitor models which arise in biology. When ε is sufficiently small, it is found that internal layers of width O(ε) appear in the u-component under the zero-flux boundary conditions, and that these layers propagate very slowly with velocity O(e-A/ε) for some positive constant A. © 1992 JJIAM Publishing Committee.
  • Kazutaka Ohara, Kazutaka Ohara, Kazutaka Ohara, Shin Ichiro Ei, Shin Ichiro Ei, Shin Ichiro Ei, Toshitaka Nagai, Toshitaka Nagai, Toshitaka Nagai  Hiroshima Mathematical Journal  22-  365  -386  1992/01   [Not refereed] [Not invited]  
    We are concerned with an ecological model described by a nonlinear diffusion equation with a nonlocal convection. The conditions under which stationary solutions exist are investigated. We also discuss the stability problem of stationary solutions. © 1992, Hiroshima University. All Rights Reserved.
  • Shin Ichiro Ei, Masayasu Mimura  Journal of Dynamics and Differential Equations  4-  191  -229  1992/01   [Not refereed] [Not invited]  
    Combustion processes are classified into three types depending upon the amount of fuel supply: two of them are the stationary states with either low or high temperatures and the other is the periodic state with relaxation oscillation type. We analyze the dependency of these processes on the amount of fuel supply by using the fast and slow dynamics approach. © 1992 Plenum Publishing Corporation.
  • 栄 伸一郎  応用数理  1-  (4)  350  -351  1991/12   [Not refereed] [Not invited]
  • M. Mimura, S. I. Ei, Q. Fang  Journal of Mathematical Biology  29-  219  -237  1991/01   [Not refereed] [Not invited]  
    We discuss a competition-diffusion system to study coexistence problems of two competing species in a homogeneous environment. In particular, by using invariant manifold theory, effects of domain-shape are considered on this problem. © 1991, Springer-Verlag. All rights reserved.
  • Two-timing methods with applications to nonlinear parabolic equations
    EI Shin-Ichiro  1991   [Not refereed] [Not invited]
  • Ei Shin-Ichiro  RIMS Kokyuroku  730-  41  -60  1990/10   [Not refereed] [Not invited]
  • S. I. Ei, M. Mimura, S. Takigawa  Japan J. Applied Mathematics  6-  223  -244  1989/06   [Not refereed] [Not invited]  
    A size-space distribution model of biological individuals including two effects of density-dependent growth rates for size and chemotactic aggregation for space is proposed. Assuming that the spatial movement is rapid in comparison with the growth process, we use time-scaling arguments to reduce the model to an approximating system of only size distribution. By the analysis of this simplified system, the dependence of these effects on extinction and existence of the individuals can be studied. © 1989 JJAM Publishing Committee.
  • Shin Ichiro Ei, Masayasu Mimura  Hiroshima Mathematical Journal  14-  649  -678  1985/01   [Not refereed] [Not invited]  
    We consider initial-boundary value problems for heterogeneous reactiondiffusion equations(formula presented) and study transient and ot ox ox large time behaviors of solutions. Our method is to explicitly construct a twotiming function u(t, ϵt, x) that converges to the exact solution as ϵ ↓ 0 uniformly in ϵ[0, ∞). Such an explicit expression of approximate solutions in terms of twotiming functions can be applied to a fairly general class of equations of the above form as well as weakly-coupled systems of such equations. © 1980, Pacific Journal of Mathematics.
  • Phase dynamics on the modified oscillators in Bipedal locomotion
    Wulin Weng, Shin-Ichiro Ei , Kunishige Ohgane   [Not refereed] [Not invited]  Other article
  • Segregating pattern problem in competition-diffusion systems
    J. Interfaces and Free Boundaries  1-  57  -80  1999   [Not refereed] [Not invited]
  • Slow dynamics of in terfaces in the Allen-Cahn eguation on a strip-like domain
    SIAM J. Math. Anal.  (29)  3,555  1998   [Not refereed] [Not invited]
  • Dynamics of Interfaces in a Scalar Parabolic equation with Variable coefficients
    Japan J. Indust. and Appl. Math.  14-  (1)  1  1997   [Not refereed] [Not invited]
  • Instability of stationary solutions for equations of curvature-driven motion of curve
    Journal of Dynamics aed Differential Equations  7-  (3)  423  1995   [Not refereed] [Not invited]
  • Stability of stationary interfaces in a generalized mean curvature flow
    J. Fac. Sci. Univ. Tokyo Sec. IA  40-  (3)  651  1994   [Not refereed] [Not invited]
  • Relaxation Oscillations in Clmbustion Models of Thermal Self-Ignition
    J. Dynamics and Differrntial Eguations  4-  (1)  1991   [Not refereed] [Not invited]
  • Pattern Formation in Heterogeneous Reaction-Diffusion-Advection System with an Application to Population Dynamics
    SIAM J. Mathermatical Analysis  21-  1990   [Not refereed] [Not invited]
  • Two-timing Methods with Applications to Heterogeneous Reaction-Diffusion Systems
    Hiroshima Mathematical J.  18-  1988   [Not refereed] [Not invited]
  • Transient and Large Time Behavior of Solutions to Heterogenlous Reaction-Diffusion Eguaions
    Hiroshima Mathematical J.  14-  1984   [Not refereed] [Not invited]

Research Grants & Projects

  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(挑戦的萌芽研究)
    Date (from‐to) : 2009 -2011 
    Author : Shin-ichiro EI
     
    九州大学By considering the neighborhood of a bifurcation point, we dealt with pulses with slow velocities and investigated the effects of geometrical properties of domains on pulse motions. In fact, general methods to derive the equations of motions were established and they were applied to problems of moving pulses along boundaries, in thin domains and on inhomogeneous media.
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2004 -2007 
    Author : Shin-ichiro EI
     
    横浜市立大学->九州大学In the period of this project, we completely classified the bifurcation structures of 1 dimensional traveling front solutions and analyzed the dynamics of traveling front solutions in inhomogeneous media from the dynamical system point of view. By the analysis, we can know how the solutions go through or reflect by obstacles with words of invariant manifold theory. The interaction of two front solutions is also treated. In general, the treatment of pulse solution is difficult. Applying the results of the interaction of two front solutions, we construct a pulse solution as the combination of...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2000 -2003 
    Author : Shin-ishiro EI
     
    横浜市立大学In this project, we considered the localized patterns in reaction-diffusion systems and tried to establish the theories to analyze the time evolutional behaviors. As the consequence, we obtained several results for the systems in 1D problems such as the bifurcation structures and pulse interactions. Explicitly speaking, he tails of pulse-like localized patterns are exponentially decaying, then we derived the equations describing the motion of interacting pulses as well as the mathematical validity. Moreover, by considering them in the neighborhood of bifurcation points and applying the stan...
  • Nonlinear Partial Diflerential Equations

Educational Activities

Teaching Experience

  • Analytic Studies
    開講年度 : 2017
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 非線形性、パターン形成, 反応拡散系
  • Introduction to Mathematics
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 微分方程式, 変数分離形, 線形方程式, 微分方程式の応用, 力学系
  • Advanced Mathematical Analysis
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 非線形性、パターン形成, 反応拡散系
  • Calculus I
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 数列, 収束, 関数, 極限, 微分, 偏微分, テイラ-の定理
  • Calculus II
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 原始関数, 積分, 重積分, リ-マン和, 変数変換
  • Basic Mathematical Science
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 坂井:確率論,統計力学,線形高分子,ランダムウォーク,自己回避歩行,臨界点,臨界現象. 栄:微分方程式, 散逸構造, 形態形成, 進行波. Jusup: conservation laws, entropy, density effects, competition, natural selection, tolerance, tipping points.

Others

  • 2017/10  Patterns and dynamics with nonlocal effect, CREST WS
  • 2017/10  New mathematical approaches for understanding of biological phenomena
  • 2017/10  formation problems with non-local effects
  • 2017/08  One-day Workshop on Reaction-Diffusion Equations at Asahikawa 2
  • 2016/08  Patterns and Waves 2016
  • 2016/07  Joint Australia-Japan workshop on dynamical systems with applications in life sciences
  • 2015/11  The 11th HU and SNU Symposium on Mathematics,Mathematical analysis and applications
  • 2015/08  Mathematical Modeling and the analysis in dissipative systems 
    Organizers: SHIN-ICHIRO EI*; Masaharu Nagayama (10665; 10756) Date: August 14 Time: 13:30--15:30 Room: Room 9 , Date: August 14 Time: 16:00--18:00 Room: Room 9 Minisymposia in The 8th International Congress on Industrial and applied mathematics, August 10-14, 2015, Beijing, China.
  • 2015/07  One-day Workshop on Reaction-Diffusion Equations at Asahikawa from Wednesday afternoon 
    July 15th to Thursday morning, July 16th, 2015 Place: Asahikawa Medical University, 2-1-1-1, Midorigaoka-higashi, Asahikawa 078-8510, Japan, Organizers: Takashi Teramoto, School of Medicine, Asahikawa Medical University, Shin-Ichiro Ei, Department of Mathematics, Hokkaido University 5名参加.
  • 2011/09  Nonlinear dynamics in partial differential equations
  • 2010/06  World of Emerging Phenomena 2


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