Shuichi Jimbo |

Faculty of Science Mathematics Mathematics |

Professor |

Last Updated :2020/09/10

- Birth:Asahikawa 1958, Professor of Hokkaido Univ., Speciality:Applied Analysis

- 2006/04 - Today Hokkaido University Department of Mathematics Faculty of Science Professor
- 1999/04 - 2006/03 Hokkaido University Department of Mathematics, Faculty of Science Professor
- 1995/04 - 1999/03 Hokkaido University Department of Mathematics, Faculty of Science Associate Professor
- 1993/04 - 1995/03 Hokkaido University Department of Mathematics, Faculty of Science Associate Professor
- 1992/04 - 1993/03 Okayama University Department of Mathematics College of Liberal Arts and Sciences Associate Professor
- 1990/04 - 1992/03 Okayama University Department of Mathematics College of Liberal Arts and Sciences Lecturer
- 1987/04 - 1990/03 The University of Tokyo Department of Mathematics Faculty of Science Assistant Professor

- 1981/04 - 1987/03 the University of Tokyo Graduate School of Science Department of Mathematics
- 1979/04 - 1981/03 The University of Tokyo Faculty of Science Department of Mathematics
- 1977/04 - 1979/03 The University of Tokyo Faculty of General Education Division of Science

**Asymptotic behavior of eigenfrequencies of a thin elastic rod with non-uniform cross-section**Shuichi JIMBO, Albert RODRIGUEZ MULETJournal of Mathematical Society of Japan 72 (1) 119 - 154 2020/01 [Refereed][Not invited]**Entire solutions to reaction-diffusion equations in multiple half-lines with a junction**Shuichi Jimbo, Yoshihisa MoritaJournal of Differential Equations 267 1247 - 1276 2019 [Refereed][Not invited]- Shuichi Jimbo, Yoshihisa MoritaJAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 34 (2) 555 - 584 0916-7005 2017/08 [Refereed][Not invited]

We deal with a generalized phase-field-type system that arises as a transformed system of reaction-diffusion equations with a conservation law. We consider the stationary problem which is reduced to a scalar elliptic equation with a nonlocal term, and study the linearized eigenvalue problem. We first prove by the spectral comparison argument that the number of unstable eigenvalues for the problem coincides with the one of the linearized eigenvalue problem for the original system. We next show a limiting behavior of eigenvalues for the scalar problem as the coefficient of the nonlocal term goes to infinity. - Shuichi Jimbo, Hideo Kozono, Yoshiaki Teramoto, Erika UshikoshiMATHEMATISCHE ANNALEN 368 (1-2) 877 - 884 0025-5831 2017/06 [Refereed][Not invited]

Based on the explicit representation of the Hadamard variational formula [1] for eigenvalues of the Stokes equations, we investigate the geometry of the domain in R-3. It turns out that if the first variation of some eigenvalue of the Stokes equations for all volume preserving perturbations vanishes, then the domain is necessarily diffeomorphic to the 2-dimensional torus T-2. - Shuichi Jimbo, Kazuhiro KurataINDIANA UNIVERSITY MATHEMATICS JOURNAL 65 (3) 867 - 898 0022-2518 2016 [Refereed][Not invited]

We study the eigenvalue problem of the Laplacian on a thin domain under a mixed boundary condition by using a pure variational approach. We obtain the detailed asymptotic behavior of such eigenvalues when the domain becomes thinner and shrinks to a surface, and we establish the characteristic geometric dependency. Furthermore, we also present an application to a certain bifurcation problem arising in population dynamics. - Chao-Nien Chen, Shuichi Jimbo, Yoshihisa MoritaNONLINEARITY 28 (4) 1003 - 1016 0951-7715 2015/04 [Refereed][Not invited]

In the study of stationary problems of the FitzHugh-Nagumo activator-inhibitor system, based on a variational structure, the associated Euler-Lagrange equation is an elliptic equation with a non-local term. We are concerned with the influence of such a variational structure on the local or global dynamics of the system. With the aid of spectral comparison, it will be shown that the dimension of the unstable manifold of an equilibrium solution to the system can actually be determined by the Morse index of the corresponding critical point. Also, some estimates for the eigenvalues concerned with the linearized stability are established. Besides the local structure near the equilibrium solutions, the existence of a Lyapunov function leads to a gradient-like property in the global dynamics. The case under consideration is when, in the equation for the inhibitor, the rate of degradation is relatively higher than that of production due to the activator. **Eigenvalues of the Laplacian in a domain with a thin tubular hole**Shuichi JimboJ. Elliptic, Parabolic, Equations 1 137 - 174 2015 [Refereed][Not invited]**Hadamard variational formula for the eigenvalue of the Stokes equations with the Dirichlet boundary conditions**Shuichi Jimbo, Erika UshikoshiFar East J. Math. 98 713 - 739 2015 [Refereed][Not invited]- Shuichi Jimbo, Yoshihisa MoritaJOURNAL OF DIFFERENTIAL EQUATIONS 255 (7) 1657 - 1683 0022-0396 2013/10 [Refereed][Not invited]

We are dealing with a two-component system of reaction-diffusion equations with mass conservation in a bounded domain with the Neumann boundary conditions. We prove the global boundedness of the solution in L-infinity-norm for t >= 0 under a condition, and then the existence of a Lyapunov function. Moreover, by studying the linearized eigenvalue problem of a nonconstant equilibrium solution, we provide a comparison theorem for the spectrum between the linearized operators of the system and an appropriate nonlocal scalar equation. As an application of the comparison result we obtain that any stable equilibrium solution must be monotone if the space dimension is one. It is also shown that a modified system with a new parameter, which covers the present model, possesses a Lyapunov function. (c) 2013 Elsevier Inc. All rights reserved. **Hadamard variation and electromagnetic frequencies**Shuichi JimboGeometric Properties for Parabolic and Elliptic PDE's, R.Magnanini et al (eds.) INdAM series 2 179 - 200 2013 [Refereed][Not invited]- A non-destructive method for damage detection in steel-concrete structures based on finite eigendataShuichi Jimbo, Antonino Morassi, Gen Nakamura, Kenji ShirotaINVERSE PROBLEMS IN SCIENCE AND ENGINEERING 20 (2) 233 - 270 1741-5977 2012 [Refereed][Not invited]

This article proposes a non-destructive method for damage detection in steel-concrete beams based on finite spectral data associated with a given set of boundary conditions. The inverse problem consists of determining two stiffness coefficients of the connection between the steel beam and the concrete beam. The inverse problem is transformed to a variational problem for a cost function which includes eigenvalue data and transversal displacements of eigenfunctions. A projected gradient method which uses the analytical expressions of the first partial derivatives of the eigenvalues and eigenfunctions is proposed for identifying the unknown coefficients. The results of an extended series of numerical simulations on real steel-concrete beams are presented and discussed. - Shuichi Jimbo, Masato Kimura, Hirofumi NotsuASYMPTOTIC ANALYSIS 65 (1-2) 103 - 123 0921-7134 2009 [Refereed][Not invited]

We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the velocity potential well condition as the parameter tends to infinity. We reveal that the depth of the potential well plays an important role in the estimate. Particularly, in one-dimensional case, we give a much more elaborate characterization for the eigenvalue. Some numerical examples are also shown. **Spectra of Domains with Partial Degeneration**Shuichi Jimbo, Satoshi KosugiJOURNAL OF MATHEMATICAL SCIENCES-THE UNIVERSITY OF TOKYO 16 (3) 269 - 414 1340-5705 2009 [Refereed][Not invited]

We consider the eigenvalue problem of the Laplacian (Neumann B.C.) in the domain which has a very thin subregion. We give a detailed characterization of the asymptotics of the eigenvalues and the eigenfunctions. The perturbation formulas take various forms depending on the type of the eigenvalue and geometric situations (dimension shape).**Ginzburg-Landau equations and solution structure**S. Jimbo, Y. MoritaSugaku Expositions 21 (2) 117 - 131 2008 [Not refereed][Not invited]- Shuichi JimboHokkaido Mathematical Journal 33 (1) 11 - 45 0385-4035 2004 [Refereed][Not invited]

We consider a (parametrized) bounded domain, some portion of which degenerates and approaches a lower dimensional set when the parameter goes to zero. We consider semilinear elliptic equation with Neumann B.C. in this domain and the behavior of the solutions in the limit. We give a characterization for the solutions in the sense of uniform convergence. © 2004 by the University of Notre Dame. All rights reserved. - S Jimbo, J ZhaiJOURNAL OF DIFFERENTIAL EQUATIONS 188 (2) 447 - 460 0022-0396 2003/03 [Refereed][Not invited]

We prove that any non-constant smooth static solution to a geometric parabolic system is unstable, provided that the domain is convex. As the important applications, we shall consider the Landau-Lifshitz equation and the heat flow for harmonic map. (C) 2002 Elsevier Science (USA). All rights reserved. - S Jimbo, S KosugiCOMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 28 (7-8) 1303 - 1323 0360-5302 2003 [Refereed][Not invited]

The asymptotic behavior of eigenvalues of an elliptic operator with a divergence form is discussed. The coefficients of the operator are discontinuous through a boundary of a subdomain and degenerate to zero on the subdomain when a parameter tends to zero. We will prove that the eigenvalues approach eigenvalues of the Laplacian on the subdomain or on the complement. We will obtain precise asymptotic behavior of their convergence. - S Jimbo, Y MoritaCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 15 (3) 325 - 352 0944-2669 2002/11 [Refereed][Not invited]

We study the Ginzburg-Landau equation with magnetic effect in a thin domain Omega(epsilon) in R-3, where the thickness of the domain is controlled by a parameter epsilon > 0. This equation is an Euler equation of a free energy functional and it has trivial solutions that are minimizers of the functional. In this article we look for a nontrivial stable solution to the equation, that is, a local minimizer of the energy functional. To prove the existence of such a stable solution in Omega(epsilon), we consider a reduced problem as epsilon --> 0 and a nondegenerate stable solution to the reduced equation. Applying the standard variational argument, we show that there exists a stable solution in Omega(epsilon) near the solution to the reduced equation if epsilon > 0 is sufficiently small. We also present a specific example of a domain which allows a stable vortex solution, that is, a stable solution with zeros. - S Jimbo, P SternbergSIAM JOURNAL ON MATHEMATICAL ANALYSIS 33 (6) 1379 - 1392 0036-1410 2002/08 [Refereed][Not invited]

Recent works have demonstrated the existence of nontrivial stable critical points of the Ginzburg Landau energy (Psi, A) -->(Z) (Omega)1/2\(del-iA)Psi\(2) + k(2)/4(1 - \Psi\(2))(2)dx + 1/2(Z) (Rn) \curl\A(2)dx for multiply connected domains Omega subset of R-n with n = 2 or 3 and for simply connected domains Omega that are close in L-1 to multiply connected domains. In this article we demonstrate that while there is no topological obstruction to the presence of such stable critical points, there is a geometric obstruction. Specifically, we show the nonexistence of stable critical points of this energy in two-dimensional convex domains. **Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition**S Jimbo, Y MoritaJAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 18 (2) 483 - 501 0916-7005 2001/06 [Refereed][Not invited]

This paper deals with the motion law of vortices in the limit as epsilon --> 0 of the Ginzburg-Landau equation u(t) = Deltau + (1/epsilon (2))(1 - \u\(2))u, u = (u(1),u(2))(T), in a planar contractible domain with Neumann boundary condition, where the vortices are meant by zeros of a solution. As epsilon --> 0, applying the argument by Jerrard-Soner to the Neumann case yields an ordinary differential equation, called a limit equation, describing the dynamics of the vortices. We show that the limit equation can be written by using the Green function with Dirichlet condition and the Robin function of it. With this nice form we discuss the dynamics of a single or two vortices together with equilibrium states of the limit equation. In addition for. the disk domain an explicit form of the equation is proposed and the dynamics for multi-vortices is investigated.**Vortex dynamics for the Ginzburg-Landau equation with Neumann condition**Shuichi Jimbo, YoshihisaMethods and applications to Analysis 8 451 - 478 2001 [Refereed][Not invited]**Domain perturbation method and local minimizers to Ginzburg-Landau functional with magnetic effect**Shuichi Jimbo, Jian ZhaiAbstr. Appl. Anal. 5 101 - 112 2000 [Refereed][Not invited]**Stable vortex solutions to the Ginzburg-Landau equation with a variable coefficient in a disk**S Jimbo, Y MoritaJOURNAL OF DIFFERENTIAL EQUATIONS 155 (1) 153 - 176 0022-0396 1999/06 [Refereed][Not invited]

This paper deals with stable solutions with a single vortex to the Ginzburg Landau equation having a variable coefficient subject to the Neumann boundary condition in a planar dish. The equation has a positive parameter, say lambda, which will play an important role for the stability of the solution. We consider the equation with a radially symmetric coefficient in the disk and suppose that the coefficient is monotone increasing in a radial direction. Then the equation possesses a pair of solutions with a single vortex for large lambda. Although these solutions for the constant coefficient are unstable, they can be stable fur a suitable variable coefficient and large lambda. The purpose of this article is to give a sufficient condition for the coefficient to allow those solutions being stable for any sufficiently large lambda. As an application we show an example of the coefficient enjoying the condition, which has an arbitrarily small total variation. (C) 1999 Academic Press.**Stabilization of vortices in the Ginzburg-Landau equation with a variable diffusion coefficient**XY Chen, S Jimbo, Y MoritaSIAM JOURNAL ON MATHEMATICAL ANALYSIS 29 (4) 903 - 912 0036-1410 1998/07 [Refereed][Not invited]

We study equilibria of the Ginzburg-Landau equation with a variable diffusion coefficient on a bounded planar domain subject to the Neumann boundary condition. It has been previously shown that if the diffusion coefficient is constant and the ambient domain is convex, the system does not carry stable vortices in the sense that any stable equilibrium solution is a constant of modulus 1. In this article we shall prove that arbitrarily given a domain, an appropriate choice of inhomogeneous diffusion coefficient yields a stable equilibrium solution having vortices. We can even manage to make the configuration of stable vortices close to prescribed locations. Our method is to minimize the free energy functional in suitably constructed positive invariant regions for the time-dependent Ginzburg-Landau equation.- Shuichi Jimbo, Jian ZhaiJournal of the Mathematical Society of Japan 50 (3) 663 - 684 1881-1167 1998 [Refereed][Not invited]
**Ginzburg-Landau equations and stable solutions in a rotational domain**S Jimbo, Y MoritaSIAM JOURNAL ON MATHEMATICAL ANALYSIS 27 (5) 1360 - 1385 0036-1410 1996/09 [Refereed][Not invited]

The Ginzburg-Landau (GL) equations, with or without magnetic effect, are studied in the case of a rotational domain in R(3). It can be shown that there exist rotational solutions which describe the physical state of permanent current of electrons in a ring-shaped superconductor. Moreover, if a physical parameter-called the GL parameter-is sufficiently large, then these solutions are stable, that is, they are local minimizers of an energy functional (GL energy). This is proved by the spectral analysis on the linearized equation.**Stable solutions with zeros to the Ginzburg-Landau equation with Neumann boundary condition**S Jimbo, Y MoritaJOURNAL OF DIFFERENTIAL EQUATIONS 128 (2) 596 - 613 0022-0396 1996/07 [Refereed][Not invited]

This paper is devoted to the Ginzburg-Landau equation Delta Phi + lambda(1 - \Phi\(2)) Phi = 0, Phi = u(1) + iu(2) in a bounded domain Omega subset of R(n) with the homogeneous Neumann boundary condition. The previous works [12-14] showed that for large lambda there exist stable non-constant solutions with no zeros in domains, which are topologically non-trivial in a certain sense. In this aritcle it is proved that for a domain Omega containing a non-trivial domain D as a subset, there exist stable solutions with zeros provided that the volume of Omega/D is sufficiently small. (C) 1996 Academic Press, Inc.**GINZBURG-LANDAU EQUATION AND STABLE STEADY-STATE SOLUTIONS IN A NONTRIVIAL DOMAIN**S JIMBO, Y MORITA, J ZHAICOMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 20 (11-12) 2093 - 2112 0360-5302 1995 [Refereed][Not invited]

The Ginzburg-Landau equation with a large parameter is studied in a bounded domain with the Neumann B.C. It is shown that many kinds of stable non-constant solutions exist in domains with some topological condition. If the space dimension is 2 or 3 and if the domain is not simply connected, this condition holds.**STABILITY OF NONCONSTANT STEADY-STATE SOLUTIONS TO A GINZBURG-LANDAU EQUATION IN HIGHER SPACE DIMENSIONS**S JIMBO, Y MORITANONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 22 (6) 753 - 770 0362-546X 1994/03 [Refereed][Not invited]**Ordinary Differential Equations (ODEs) on Inertial Manifolds for Reaction-Diffusion Systems in a Singularly Perturbed Domain with Several Thin Channels**Y. Morita, S. JimboJ. Dynamics and Diffrential Equations 4 (1) 65 - 93 1992 [Not refereed][Not invited]**Remarks on the Behavior of Certain Eigenvalues on a Singularly Perturbed Domain with Several Thin Channels**S. Jimbo, Y. MoritaComm. Partial Differential Equations 17 (3-4) 523 - 552 1992 [Not refereed][Not invited]

- 神保秀一, 久保英夫
**多変数の微積分とベクトル解析**

数理工学社 2020/09 - Shuichi Jimbo (Single work)
**Introduction to Differential Equations**

Suuri Kogakusya 2018/01 - Shuichi Jimbo, Naofumi Honda (Joint workChap.1, Chap 2, Chap 5)
**Topological Space**

Sugaku Shobo 2011/04 - Shuichi Jimbo, Yoshihisa Morita (Joint workChap 3, Chap 4, Chap 5, Chap 8)
**Ginzburg-Landau equation and Stability Analysis**

Iwanami Pub. Co. 2009/05 - Shuichi Jimbo (Single workAll)
**Introduction to Partial Differential Equations**

Kyoritsu Publ. Co. 2006/08 - Shuichi Jimbo (Single workAll)
**Theory of Differential Equations**

Saiensu Co 1999/01 - Shuichi Jimbo, Rentaro Agemi, Koji Kubota, Shigeo Kato, Osamu Katsumata (Joint workChap 2)
**Integral Calculus**

Kyoritsu Publ. Co. 1995/09 - Shuichi Jimbo, Rentaro Agemi, Shigeo Kato, Koji Kubota, Keizo Yamaguchi, Osamu Katsumata (Joint workChap 2)
**Differential Calculus**

Kyoritsu Publ. Co. 1995/03

- Time entire solution of the Allen-Cahn equation in the star graph [Invited]Shuichi JimboJapan Mathematical Society(Special Lecture) 2019/09
- Spectral properties of thin elastic rod - modes of bending, torsion and stretching [Invited]Shuichi JimboPDE on thin domains and related topics (Tokyo Metropolitan Univ.) 2019/09
- Y-shaped graph and time entire solutions of the Allen-Cahn equation [Invited]Shuichi JimboWorkshop on New Trends in Variational Models,Fields Institute, Toronto Univ. 2019/06
- Y-shaped graph and time entire solutions of a semilinear parabolic equation [Invited]Shuichi JimboReaction-Diffusion Equation - Analysis on Propagation phonemena and Singularities and its Application to Sciences, RIMS, Kyoto Univ. 2018/10
- Eigenvalue problem of the Laplacian in a domain with a thin tubular hole [Invited]Shuichi JimboThe third international conference on the Dynamics of Differential Equations, In memory of Prof Jack Hale, Hiroshima Univ. 2018/03
- Y-shaped graph and time entire solutions of a semilinear parabolic equation [Invited]Shuichi JimboDifferential Equations and Networks, Tohoku Univ. 2018/01
- Y shaped graph and reaction diffusion equation [Invited]Shuichi JimboQualitative Theory on Nonlinear Partial Differential Equations, Okayama Univ. 2017/09
- Y字形グラフと反応拡散方程式 [Not invited]神保秀一非線形現象の数値シミュレーションと解析 2017, 北大理 2017/03
- Y-shaped graph and time entire solutions of a semilinear parabolic equation [Invited]Shuichi JimboGeometry of solutions of PDE's and its related inverse problem, Tohoku Univ. 2016/10
- 特異的領域変形と固有値問題 [Invited]神保秀一パターン形成とダイナ ミクスの解構造の探求, 北大 2015/06
- Eigenvalues of Laplacian in a domain with a thin tubular hole [Invited]Shuichi JimboNCTS Workshop on Calculus of Variations and Related Topics, National TsinHua Univ.Taiwan 2014/10
- Eigenvalues of the Laplacian in a domain with a thin tubular hole [Invited]Shuichi Jimbo8th European Conference on Elliptic and Parabolic Problems,Gaeta 2014/05
- Domain variation and electromagnetic frequencies [Invited]Shuichi JimboNortheastern Conference on Mathematical Analysis, Tohoku Univ. 2013/02
- 弾性体方程式の固有値に関する特異摂動問題 [Invited]神保秀一第８回非線型の諸問題 2012/09
- Domain variation and electromagnetic frequencies [Invited]Shuichi JimboNonlinear partial differential equations, dynamical systems and their applications, RIMS, Kyoto Univ. 2012/09
- Eigenvalues of the Elliptic operator including a large nonlocal term [Invited]Shuichi JimboSeol University Hokkaido University joint seminar 2011/11
- Domain Variation and Electromagnetic Frequencies [Invited]Shuichi JimboGeometric properties for Parabolic and Elliptic PDE's, 2nd Italian-Japanese Workshop, INdAM Workshop 2011/06
- Singular perturbation of domains and the characterization of the behavior of the eigenvalues in several elliptic operators [Invited]Shuichi Jimbo2010 NCTS workshop on Calculus of Variation and related topics National Tsing Hua University, Hsinchu, Taiwan 2010/05
- Electromagnetic oscillation in a domain with a small hole [Not invited]Shuichi JimboNew Developments of Functional Equations in Mathematical Analysis, RIMS Kyoto Univ. 2009/11
- Vortex motion in Ginzburg-Landau equation [Not invited]Shuichi JimboAnalytic semigroups and related topics - on the occasion of the centenary of the birth of Professor K\^osaku Yosida, Univ. Tokyo 2009/01
- Spectra domains with partial degeneration [Invited]Shuichi JimboPDEセミナー國立彰化師範大学 2008/12
- Eigenvalues of elliptic operators with variable coefficients in domains with small holes or thin tunnels [Invited]Shuichi JimboPDEセミナー, 國立中山大学(高雄) 2008/12
- Spectral analysis of elliptic operators on a singularly perturbed domains [Not invited]Shuichi JimboPDE seminar, Zhejiang University 2008/11
- Spectral property of a singularly perturbed domain - Perturbation of the resonant eigenvalues [Invited]Shuichi JimboSeol University Hokkaido University joint seminar 2008/01
- Spectra of domains with partial degeneration [Not invited]Shuichi Jimbo数学綜合報告会, 復旦大学数学科学学院 2007/09
- Ginzburg-Landau equations in thin domains [Not invited]Shuichi JimboInternational Conference on Mathematical Theory of Superconductivity and Liquid Crystal, East China Normal University 2007/05

- 神保 秀一 数理解析研究所講究録 1702- (0) 88 -97 2010/08 [Not refereed][Not invited]
- JIMBO Shuichi Mathematics Education Society of Japan, Japan journal of mathematics education and related fields 46- (3) 25 -29 2006/03/26 [Not refereed][Not invited]
- 神保 秀一, 岩井 泰夫, 大矢 二郎, 平野 葉一 数学教育学会誌. 臨時増刊, 数学教育学会発表論文集 2004- (2) 43 -45 2004/09/19 [Not refereed][Not invited]
- Jimbo Shuichi Bulletin of the Japan Society for Industrial and applied Mathematics 12- (1) 75 -77 2002/03/15 [Not refereed][Not invited]
- Jimbo Shuichi RIMS Kokyuroku 1237- (0) 208 -215 2001/11 [Not refereed][Not invited]
- Jimbo Shuichi Bulletin of the Japan Society for Industrial and applied Mathematics 11- (2) 152 -162 2001/06 [Not refereed][Invited]

I describe recent studies on Ginzburg-Landau equation and behavior of vortices under singular perturbation situation. Each vortex carries a quantized energy of amountπ log (1/ε) +0(1). The behavior of the vortices can be described in terms of ODE with the aid of a finite dimensional Potential function, which is called the renormalized energy. Examples of vortex motion in the case of disk with Neumann boundary condition are explained and the total dynamics are solved. - Jimbo Shuichi RIMS Kokyuroku 1111- (0) 102 -106 1999/08 [Not refereed][Not invited]
- Jimbo Shuichi, Morita Yoshihisa RIMS Kokyuroku 1025- (0) 35 -43 1998/02 [Not refereed][Not invited]
- JIMBO SHUICHI, ZHAI JIAN RIMS Kokyuroku 951- (0) 21 -27 1996/05 [Not refereed][Not invited]
- Zhai Jian RIMS Kokyuroku 913- (0) 68 -81 1995/06 [Not refereed][Not invited]

**Elliptic system of equations in singular or extreme shaped domains**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban CDate (from‐to) : 2016/04 -2019/03Author : Shuichi Jimbo**Domain deformation and analysis on elliptic operators in the oscillation problems in elastic bodies and electromagnetic fields**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban CDate (from‐to) : 2013/04 -2016/03Author : Shuichi Jimbo**Lam\'e Operator in a complex domain**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban CDate (from‐to) : 2010/04 -2013/03Author : Shuichi Jimbo**Asymptotic analysis of elliptic operators with singular deformation of domains and degeneration of coefficients**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban BDate (from‐to) : 2005/04 -2009/03Author : Shuichi Jimbo**Singular deformation of domains and spectral analysis of electro-magnetic problem**Japan Society of Promotion of Sciences：JSPS Kakenhi HougaDate (from‐to) : 2003/04 -2006/03Author : Shuichi Jimbo**Analysis on PDEs in Material Sciences**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban CDate (from‐to) : 2001/04 -2003/03Author : Shuichi Jimbo**Nonlinear PDEs and infinite dimensional dynamical systems**Japan Society of Promotion of Sciences：JSPS Kakenhi Kiban BDate (from‐to) : 1997/04 -2000/03Author : Shuichi Jimbo**Variational problems in the models of the Liquid Crystals**Japan Society of Promotion of Sciences：JSPS Kakenhi HougaDate (from‐to) : 1997/04 -1999/03Author : Shuichi Jimbo

- Analytic Studies開講年度 : 2018課程区分 : 修士課程開講学部 : 理学院キーワード : 非線形性、微分方程式、力学系, フラクタル、分岐現象
- Advanced Mathematical Analysis開講年度 : 2018課程区分 : 学士課程開講学部 : 理学部キーワード : 非線形性、微分方程式、力学系, フラクタル、分岐現象
- Calculus I開講年度 : 2018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, 極値問題
- Calculus II開講年度 : 2018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