研究者データベース

劉 逸侃(リユウ イツカン)
電子科学研究所 附属社会創造数学研究センター
助教

基本情報

所属

  • 電子科学研究所 附属社会創造数学研究センター

職名

  • 助教

学位

  • 博士(数理科学)(東京大学大学院数理科学研究科)

J-Global ID

研究キーワード

  • 数理モデリング   偏微分方程式   逆問題   

研究分野

  • 自然科学一般 / 数理解析学 / 応用解析

職歴

  • 2019年08月 - 現在 北海道大学 電子科学研究所 助教
  • 2018年07月 - 2019年07月 東京大学 大学院数理科学研究科 特任助教
  • 2016年11月 - 2018年06月 東京大学 大学院数理科学研究科 学振外国人特別研究員
  • 2015年04月 - 2016年10月 東京大学 大学院数理科学研究科 特任研究員

学歴

  • 2011年04月 - 2015年03月   東京大学   大学院数理科学研究科   数理科学

所属学協会

  • 日本応用数理学会   日本数学会   

研究活動情報

論文

  • Yavar Kian, Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
    Mathematische Annalen 380 3-4 1465 - 1495 2021年08月 [査読有り][通常論文]
     
    This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional time-fractional evolution equation either in a Euclidean domain or on a Riemannian manifold. Based on a special choice of the Dirichlet boundary input, we prove the unique recovery of at most two out of four x-dependent coefficients (possibly with an extra unknown fractional order) by a single measurement of the partial Neumann boundary output. Especially, both a vector-valued velocity field of a convection term and a density can also be uniquely determined. The key ingredient turns out to be the time-analyticity of the decomposed solution, which enables the construction of Dirichlet-to-Neumann maps in the frequency domain and thus the application of inverse spectral results.
  • Yikan Liu, Guanghui Hu, Masahiro Yamamoto
    Inverse Problems 37 8 084001 - 084001 2021年08月01日 [査読有り][招待有り]
     
    This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order α ∈ (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < α ≤ 1 and 1 < α ≤ 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions.
  • Yikan Liu
    数理解析研究所講究録 2174 73 - 87 2021年02月 [査読無し][招待有り]
     
    This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on the uniqueness, we adopt a minimization procedure with regularization to construct iterative thresholding schemes for the reduced backward problems on recovering one or two unknown initial value(s). Moreover, an elliptic approach is proposed to solve a convection equation in the case of two profiles.
  • Zhiyuan Li, Xing Cheng, Yikan Liu
    Taiwanese Journal of Mathematics 24 4 1005 - 1020 The Mathematical Society of the Republic of China 2020年08月 [査読有り][通常論文]
     
    This paper deals with an inverse source problem for the multi-term time-fractional diffusion equation with a diffusion parameter by using final overdetermination. On the basis of analytic Fredholm theory, a generic well-posedness of the inverse source problem in some suitable function space is proved.
  • Daijun Jiang, Yikan Liu, Dongling Wang
    Advances in Computational Mathematics 46 3 2020年05月 [査読有り][通常論文]
     
    In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear minimization system by an appropriately selected Tikhonov regularization. The existence and the stability of the optimization system are demonstrated. The nonlinear optimization problem is approximated by a fully discrete scheme, whose convergence is established under a novel result verified in this study that the H1-norm of the solution to the discrete forward system is uniformly bounded. The iterative thresholding algorithm is proposed to solve the discrete minimization, and several numerical experiments are presented to show the efficiency and the accuracy of the algorithm.
  • Guanghui Hu, Yikan Liu, Masahiro Yamamoto
    Inverse Problems and Related Topics 310 81 - 100 2020年02月 [査読有り][招待有り]
     
    This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of R^d or in the whole space R^d. Based on a newly established fractional Duhamel's principle, we derive a Lipschitz stability estimate in the case of a localized moving source by the observation data at d interior points. The uniqueness for the general non-localized moving source is verified with additional data of more interior observations.
  • Jin Cheng, Yi-kan Liu, Yan-bo Wang, Masahiro Yamamoto
    Acta Mathematicae Applicatae Sinica, English Series 36 1 3 - 17 2020年01月 [査読有り][招待有り]
     
    In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain. Using the corresponding Riemann function, we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives. Further, we construct several examples showing the possibility of further reducing the additional information of the other component. This result possesses remarkable significance in both theoretical and practical aspects because the required data is almost halved for the unique determination of the whole solution.
  • Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
    Handbook of Fractional Calculus with Applications 2 431 - 442 2019年02月 [査読有り][招待有り]
     
    When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be directly measured, which requires one to discuss inverse problems of identifying these physical quantities from some indirectly observed information of solutions. Inverse problems in determining these unknown parameters of the model are not only theoretically interesting, but also necessary for finding solutions to initial-boundary value problems and studying properties of solutions. This chapter surveys works on such inverse problems for fractional diffusion equations.
  • Yikan Liu, Zhiyuan Li, Masahiro Yamamoto
    Handbook of Fractional Calculus with Applications 2 411 - 430 2019年02月 [査読有り][招待有り]
     
    In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order α ∈ (0, 1). Our survey covers the following types of inverse problems: - determination of time-dependent functions in interior source terms - determination of space-dependent functions in interior source terms - determination of time-dependent functions appearing in boundary conditions
  • Jie Yu, Yikan Liu, Masahiro Yamamoto
    Inverse Problems 34 4 2018年02月15日 [査読有り][通常論文]
     
    In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.
  • Yanbo Wang, Yikan Liu, Jin Cheng
    SCIENTIA SINICA MATHEMATICA 47 10 1327 - 1334 2017年10月 [査読有り][招待有り]
     
    The unique continuation for partial differential equations means that the solutions on a small domain can uniquely determine the solutions on a larger connected domain. In this note, a new unique continuation property for the Lamé system in two dimensions is studied. We prove that, if only one component of the solution to a Lamé system can be measured on a small domain, the solution on a larger connected domain can be determined up to at most four constants.
  • Yikan Liu, Zhidong Zhang
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 30 2017年07月 [査読有り][通常論文]
     
    In this article, we consider the reconstruction of rho(t) in the (time-fractional) diffusion equation (partial derivative(alpha)(t) - triangle)u(x, t) = rho(t)g(x) (0 < alpha <= 1) by observation at a single point x(0). We are mainly concerned with the situation of x(0) is not an element of supp g, which is practically important but has not been well investigated in literature. Assuming finite sign changes of. and an extra observation interval, we establish the multiple logarithmic stability for the problem based on a reverse convolution inequality and a lower estimate for positive solutions. Meanwhile, we develop a fixed-point iteration for the numerical reconstruction and prove its convergence. The performance of the proposed method is illustrated by several numerical examples.
  • Daijun Jiang, Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
    INVERSE PROBLEMS 33 5 2017年05月 [査読有り][通常論文]
     
    In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.
  • Daijun Jiang, Yikan Liu, Masahiro Yamamoto
    JOURNAL OF DIFFERENTIAL EQUATIONS 262 1 653 - 681 2017年01月 [査読有り][通常論文]
     
    In this paper, we investigate the inverse problem on determining the spatial component of the source term in the hyperbolic equation with a time-dependent principal part. Based on a Carleman estimate for general hyperbolic operators, we prove a local stability result of Holder type in both cases of partial boundary and interior observation data. Numerically, we adopt the classical Tikhonov regularization to reformulate the inverse problem into a related optimization problem, for which we develop an iterative thresholding algorithm by using the corresponding adjoint system. Numerical examples up to three spatial dimensions are presented to demonstrate the accuracy and efficiency of the proposed algorithm. (C) 2016 Elsevier Inc. All rights reserved.
  • Yikan Liu
    COMPUTERS & MATHEMATICS WITH APPLICATIONS 73 1 96 - 108 2017年01月 [査読有り][通常論文]
     
    In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, we prove the uniqueness for determining the temporal component of the source term with the help of the fractional Duhamel's principle for the multi-term case. (C) 2016 Elsevier Ltd. All rights reserved.
  • Daijun Jiang, Yikan Liu, Masahiro Yamamoto
    MATHEMATICAL ANALYSIS OF CONTINUUM MECHANICS AND INDUSTRIAL APPLICATIONS 26 153 - 164 2017年 [査読有り][通常論文]
     
    In this chapter, we study the inverse problem on recovering a spatial component of the source term in a wave equation by the final observation data. Employing the analytic Fredholm theory, we establish a generic well-posedness result concerning the uniqueness of our inverse source problem. Numerically, by treating a corresponding minimization problem, we investigate the variational equation for the minimizer and develop an iterative thresholding algorithm. One- and two-dimensional numerical experiments are implemented to demonstrate the robustness and accuracy of the proposed algorithm.
  • Yikan Liu, William Rundell, Masahiro Yamamoto
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS 19 4 888 - 906 2016年08月 [査読有り][通常論文]
     
    The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish a strong maximum principle for time-fractional diffusion equations with Caputo derivatives, which is slightly weaker than that for the parabolic case. As a direct application, we give a uniqueness result for a related inverse source problem on the determination of the temporal component of the inhomogeneous term.
  • Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
    APPLIED MATHEMATICS AND COMPUTATION 257 381 - 397 2015年04月 [査読有り][通常論文]
     
    In this paper, we investigate the well-posedness and the long-time asymptotic behavior for initial-boundary value problems for multi-term time-fractional diffusion equations. The governing equation under consideration includes a linear combination of Caputo derivatives in time with decreasing orders in (0,1) and positive constant coefficients. By exploiting several important properties of multinomial Mittag-Leffler functions, various estimates follow from the explicit solutions in form of these special functions. Then we prove the uniqueness and continuous dependency on initial values and source terms, from which we further verify the Lipschitz continuous dependency of solutions with respect to coefficients and orders of fractional derivatives. Finally, by a Laplace transform argument, it turns out that the decay rate of the solution as t -> infinity is given by the minimum order of the time-fractional derivatives. (C) 2014 Elsevier Inc. All rights reserved.
  • 相転移と特異拡散に対する数学解析と数値解法について
    劉 逸侃
    東京大学 2015年03月 [査読有り][通常論文]
  • Bangti Jin, Raytcho Lazarov, Yikan Liu, Zhi Zhou
    JOURNAL OF COMPUTATIONAL PHYSICS 281 825 - 843 2015年01月 [査読有り][通常論文]
     
    We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates. (C) 2014 The Authors. Published by Elsevier Inc.
  • Yikan Liu, Daijun Jiang, Masahiro Yamamoto
    SIAM JOURNAL ON APPLIED MATHEMATICS 75 6 2610 - 2635 2015年 [査読有り][通常論文]
     
    In this paper, we consider the reconstruction of the nucleation rate in the three-dimensional time cone model, which turns out to be an inverse source problem for a double hyperbolic equation. More precisely, we attempt to recover a spatial component of the nucleation rate by partial interior observation data. After a direct derivation of a hyperbolic-type governing equation from the original model, we establish the well-posedness result for the forward problem by the classical hyperbolic theory. To guarantee the validity of the reconstruction, we prove the two-sided global Lipschitz stability for the inverse problem based on a Carleman estimate. Motivated by the iterative thresholding algorithm for the same problem for hyperbolic equations, we develop an iterative thresholding algorithm for the identification. Extensive numerical experiments up to three spatial dimensions demonstrate the efficiency and accuracy of the algorithm, and detailed analysis of the computational performance is also provided.
  • Yikan Liu, Masahiro Yamamoto
    APPLICABLE ANALYSIS 93 6 1297 - 1318 2014年06月 [査読有り][通常論文]
     
    We discuss Cahn's time cone method modelling phase transformation kinetics. The model equation by the time cone method is an integral equation in the space-time region. First, we reduce it to a system of hyperbolic equations, and in the case of odd spatial dimensions, the reduced system is a multiple hyperbolic equation. Next, we propose a numerical method for such a hyperbolic system. By means of alternating direction implicit methods, numerical simulations for practical forward problems are implemented with satisfactory accuracy and efficiency. In particular, in the three dimensional case, our numerical method on the basis of reduced multiple hyperbolic equation is fast.
  • Yikan Liu, Xiang Xu, Masahiro Yamamoto
    INVERSE PROBLEMS 28 9 2012年09月 [査読有り][通常論文]
     
    Nucleation and growth mechanisms are important kinetics of the phase transformation model which arises in the crystallization of polymer materials. In each stage, the nucleation rate and growth rate are crucial coefficients describing the kinetics of the process as well as the properties of the specimens. Moreover, the identification of these physical parameters describing the nucleation or the growth mechanisms is essential for controlling the crystallization of polymers and so is a significant subject also from an industrial viewpoint. In this paper, we show that we can re-formulate the time cone approach of Cahn (1996 Mater. Res. Soc. Symp. Proc. 398 425-37) by a hyperbolic governing equation with the heterogeneous nucleation rate and spatially homogeneous growth rate. Then, on the basis of the hyperbolic equation, we investigate an inverse problem of determining the growth rate for an isothermal one-dimensional specimen. Our inverse problem is an inverse coefficient problem for a hyperbolic equation which is highly nonlinear with respect to the observation data. A two-step Tikhonov-type regularization method is proposed to reconstruct the growth rate provided with the final noisy observation data. Numerical prototype examples are presented to illustrate the validity and effectiveness of the proposed scheme.
  • 組織生成をモデル化する双曲系の順問題と逆問題
    劉 逸侃
    東京大学 2012年03月 [査読有り][通常論文]

書籍

  • 統計と計算逆問題
    劉 逸侃, 徐 定華, 程 晋 (担当:共訳)
    科学出版社 2018年08月 (ISBN: 9787030581815) 295

講演・口頭発表等

  • 劉 逸侃
    日本数学会2021年度秋季総合分科会 2021年09月 口頭発表(一般)
  • (時間非整数階) 発展方程式における移動する源泉項の形状決定について  [通常講演]
    Guanghui Hu, 劉 逸侃, 山本昌宏
    2020年度応用数学合同研究集会 2020年12月 口頭発表(一般)
  • Uniqueness for determining profiles of moving sources in (time-fractional) evolution equations  [招待講演]
    劉 逸侃
    The Workshop on Theoretical and Computational Analyses for Inverse Problems 2020年12月 口頭発表(招待・特別)
  • Inverse moving source problems on determining profiles in (time-fractional) evolution equations  [招待講演]
    劉 逸侃
    Workshop on Inverse Problems 2020年10月 口頭発表(招待・特別)
  • Uniqueness and numerical schemes for an inverse moving source problem for (time-fractional) evolution equations  [招待講演]
    劉 逸侃
    4th Conference on Numerical Methods for Fractional-Derivative Problems 2020年10月 口頭発表(招待・特別)
  • 非整数階時間微分をもつ拡散方程式における源泉項の空間成分の数値再構成について  [通常講演]
    Daijun Jiang, 劉 逸侃, Dongling Wang
    日本応用数理学会2020年度年会 2020年09月 口頭発表(一般)
  • Inverse moving source problems for (time-fractional) evolution equations  [招待講演]
    劉 逸侃
    北陸応用数理研究会2020 2020年02月 口頭発表(一般)
  • 非整数階発展方程式とその逆問題について  [招待講演]
    劉 逸侃
    北海道大学数学教室談話会 2020年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Inverse moving source problems for (time-fractional) diffusion(-wave) equations  [招待講演]
    劉 逸侃
    偏微分方程式による逆問題解析とその周辺 2020年01月 口頭発表(一般)
  • Unique continuation property for two-dimensional anisotropic elasticity systems with partial information  [通常講演]
    劉 逸侃
    2019年度応用数学合同研究集会 2019年12月 口頭発表(一般)
  • Inverse source problems for time-fractional evolution equations  [通常講演]
    劉 逸侃
    2019 International Symposium of RIES and CEFMS 2019年12月 ポスター発表
  • Inverse source problems for time-fractional evolution equations  [通常講演]
    劉 逸侃
    第20回電子研国際シンポジウム 2019年12月 ポスター発表
  • Inverse problems for hyperbolic-type equations with time-dependent principal parts  [招待講演]
    劉 逸侃
    Workshop on PDEs in Direct and Inverse Problems 2019 2019年11月 口頭発表(招待・特別)
  • A concise review on inverse problems for time-fractional evolution equations  [招待講演]
    劉 逸侃
    2019年11月 公開講演,セミナー,チュートリアル,講習,講義等
  • General introduction to inverse problems for time-fractional evolution equations  [招待講演]
    劉 逸侃
    Forum on Inverse Problems 2019年11月 口頭発表(一般)
  • Inverse source problems for time-fractional diffusion(-wave) equations  [招待講演]
    劉 逸侃
    Inverse Problems and Related Fields '19 2019年11月 口頭発表(招待・特別)
  • Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement  [招待講演]
    劉 逸侃
    Workshop on Optimal Control and Optimization for Nonlocal Models 2019年10月 口頭発表(一般)
  • Determination of an orbit in the moving source of a (time-fractional) diffusion(-wave) equation  [通常講演]
    劉 逸侃
    The 5th International Symposium on Inverse Problems, Design and Optimization 2019年09月 口頭発表(一般)
  • A concise review on inverse problems for fractional diffusion equations  [招待講演]
    劉 逸侃
    2019年09月 公開講演,セミナー,チュートリアル,講習,講義等
  • Orbit determination in an inverse moving source problem for fractional diffusion(-wave) equations  [招待講演]
    劉 逸侃
    Workshop for Young Scholars "Control and Inverse Problems on Waves, Oscillations and Flows -Mathematical Analysis and Computational Methods-" 2019年08月 口頭発表(一般)
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [通常講演]
    劉 逸侃
    Summer School on Applied Inverse Problems and Related Topics 2019年08月 口頭発表(一般)
  • Mathematical analyses for inverse problems for fractional diffusion equations  [通常講演]
    劉 逸侃
    The 9th International Congress on Industrial and Applied Mathematics 2019年07月 口頭発表(一般)
  • Multiple hyperbolic systems modeling the phase transformation and related inverse problems  [招待講演]
    劉 逸侃
    2019年06月 公開講演,セミナー,チュートリアル,講習,講義等
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [招待講演]
    劉 逸侃
    2019年06月 公開講演,セミナー,チュートリアル,講習,講義等
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [通常講演]
    劉 逸侃
    The 11th Annual Meeting on Inverse Problems in China 2019年06月 口頭発表(一般)
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [通常講演]
    劉 逸侃
    The 14th SIAM East Asian Section Conference 2019年06月 口頭発表(一般)
  • Identification of the temporal component in the source term of a (time-fractional) diffusion equation  [通常講演]
    劉 逸侃
    3rd Workshop on Numerical Methods for Fractional-Derivative Problems 2019年04月 口頭発表(一般)
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [招待講演]
    劉 逸侃
    2019年04月 公開講演,セミナー,チュートリアル,講習,講義等
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [招待講演]
    劉 逸侃
    2019年04月 公開講演,セミナー,チュートリアル,講習,講義等
  • Multiple hyperbolic systems modeling the phase transformation and related inverse problems  [招待講演]
    劉 逸侃
    HMMCセミナー 2019年03月 公開講演,セミナー,チュートリアル,講習,講義等
  • Maximum principle for time-fractional diffusion equations and a related inverse problem  [招待講演]
    劉 逸侃
    偏微分方程式の最大値原理とその周辺 3 2019年03月 口頭発表(一般)
  • Inverse problems for hyperbolic-type equations with time-dependent principal parts  [招待講演]
    劉 逸侃
    The 10th Annual Meeting on Inverse Problems 2018年05月 口頭発表(招待・特別)
  • A new unique continuation property for two-dimensional anisotropic elasticity systems  [通常講演]
    劉 逸侃
    9th International Conference "Inverse Problems: Modeling and Simulation" 2018年05月 口頭発表(一般)
  • Unique continuation property with partial information for two-dimensional anisotropic elasticity systems  [招待講演]
    劉 逸侃
    広島数理解析セミナー 2018年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Time-fractional diffusion equations: Maximum principle and inverse problem  [招待講演]
    劉 逸侃
    Kusatsu Seminar 2018 2018年01月 口頭発表(一般)
  • Coefficient inverse problem for hyperbolic equations with time-dependent principal parts  [通常講演]
    劉 逸侃
    Taiwan-Japan Joint Workshop on Inverse Problems 2017年11月 口頭発表(一般)
  • A new unique continuation property for anisotropic elasticity systems in two dimensions  [通常講演]
    劉 逸侃
    A3 Workshop on Modeling and Computation of Applied Inverse Problems 2017年10月 口頭発表(一般)
  • Inverse problems for the acoustic equation with a time-dependent principal part  [招待講演]
    劉 逸侃
    CSRC Summer School on Applied Inverse Problems 2017年08月 口頭発表(一般)
  • Inverse problems for hyperbolic equations  [招待講演]
    劉 逸侃
    2017年06月 公開講演,セミナー,チュートリアル,講習,講義等
  • Reconstruction of the temporal component in the source term of a fractional diffusion equation  [通常講演]
    劉 逸侃
    Applied Inverse Problem Conference 2017 2017年05月 口頭発表(一般)
  • An inverse source problem for (time-fractional) diffusion equations  [招待講演]
    劉 逸侃
    2017年05月 公開講演,セミナー,チュートリアル,講習,講義等
  • Summary of Study Group 2016: Improvement of measurement algorithms in automatic straightening machines  [通常講演]
    劉 逸侃
    Workshop on Computational Sciences and Financial Data Analysis 2016年12月 口頭発表(一般)
  • 非整数階拡散方程式のソース項決定逆問題  [通常講演]
    劉 逸侃
    日本数学会異分野・異業種研究交流会 2016年11月 ポスター発表
  • Two inverse source problems for time-fractional diffusion equations  [招待講演]
    劉 逸侃
    2nd East Asia Section of IPIA-Young Scholars Symposium 2016年11月 口頭発表(一般)
  • Two inverse source problems for time-fractional diffusion equations  [招待講演]
    劉 逸侃
    2016年10月 公開講演,セミナー,チュートリアル,講習,講義等
  • Iterative thresholding algorithm for inverse source problems for hyperbolic-type equations  [通常講演]
    劉 逸侃
    The Fifth International Conference on Continuous Optimization 2016年08月 口頭発表(一般)
  • Inverse source problems for hyperbolic-type equations with time-dependent principal parts  [招待講演]
    劉 逸侃
    The 8th International Conference on Inverse Problems and Related Topics 2016年07月 口頭発表(招待・特別)
  • Determination of the temporal component in the source term of a fractional diffusion equation  [通常講演]
    劉 逸侃
    The 8th International Conference on Inverse Problems and Related Topics 2016年06月 口頭発表(一般)
  • Inverse source problems for hyperbolic-type equations describing the time cone model  [招待講演]
    劉 逸侃
    The 8th International Workshop on Theoretical and Computational Analyses for Inverse Problems 2016年06月 口頭発表(招待・特別)
  • Strong maximum principle for fractional diffusion equations and its application to an inverse problem  [招待講演]
    劉 逸侃
    2016年04月 公開講演,セミナー,チュートリアル,講習,講義等
  • Inverse source problems for hyperbolic-type equations  [招待講演]
    劉 逸侃
    2016年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • An inverse source problem for fractional diffusion equations  [通常講演]
    劉 逸侃
    Winter School in Imaging Science 2016年01月 口頭発表(一般)
  • Hyperbolic-type equations and related inverse problems for the time cone model  [招待講演]
    劉 逸侃
    International Conference CoMFoS15: Mathematical Analysis of Continuum Mechanics and Industrial Applications 2015年11月 口頭発表(一般)
  • Inverse source problems for hyperbolic-type equations  [通常講演]
    劉 逸侃
    International Conference on Inverse Problems, Imaging, and Applications 2015年08月 口頭発表(一般)
  • Inverse source problem for a double hyperbolic equation modeling the three-dimensional time cone model  [通常講演]
    劉 逸侃
    International Workshop on Regularization Theory of Unstructured Data 2015年05月 口頭発表(一般)
  • 非整数階の時間微分項を持つ拡散方程式の初期値境界値問題について  [招待講演]
    劉 逸侃
    FMSP院生集中講義 2015年03月 公開講演,セミナー,チュートリアル,講習,講義等
  • Inverse source problem for the three-dimensional time cone model  [招待講演]
    劉 逸侃
    微分方程式の逆問題とその周辺 2015年01月 口頭発表(一般)
  • Mathematical model for phase transformation phenomena and related topics  [招待講演]
    劉 逸侃
    数学活用のための交流会 2014年12月 公開講演,セミナー,チュートリアル,講習,講義等
  • Hyperbolic-type equations and the related inverse source problems  [通常講演]
    劉 逸侃
    Seoul-Tokyo Conference on Applied Partial Differential Equations: Theory and Applications 2014年12月 口頭発表(一般)
  • Various topics on multiple hyperbolic equations and fractional diffusion equations  [通常講演]
    劉 逸侃
    A3 Foresight Program Conference on Modeling and Computation of Applied Inverse Problems 2014年11月 口頭発表(一般)
  • 相変態モデルに関する順問題と逆問題  [通常講演]
    劉 逸侃
    日本数学会異分野・異業種研究交流会 2014年10月 ポスター発表
  • Two classes of partial differential equations modeling structure generation and anomalous diffusion  [招待講演]
    劉 逸侃
    FMSP交流会 2014年07月 口頭発表(一般)
  • An efficient numerical method for inverse source problems for hyperbolic-type equations  [通常講演]
    劉 逸侃
    Recent Progress in Mathematical and Numerical Analysis of Inverse Problems 2014年05月 ポスター発表
  • Well-posedness and numerical simulation for multi-term time-fractional diffusion equations with positive constant coefficients  [招待講演]
    劉 逸侃
    2014年05月 公開講演,セミナー,チュートリアル,講習,講義等
  • Well-posedness and numerical simulation for multi-term time-fractional diffusion equations with positive constant coefficients  [招待講演]
    劉 逸侃
    2014年03月 公開講演,セミナー,チュートリアル,講習,講義等
  • Well-posedness and numerical simulation for multi-term time-fractional diffusion equations with positive constant coefficients  [通常講演]
    劉 逸侃
    異常拡散の数理とシミュレーション手法ならびに関連する課題 2014年03月 口頭発表(一般)
  • Innovation in the control software of the fully automatic straightening machine  [通常講演]
    劉 逸侃
    産業界からの課題解決のためのスタディグループ 2014年02月 口頭発表(一般)
  • Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients  [招待講演]
    劉 逸侃
    2013年10月 公開講演,セミナー,チュートリアル,講習,講義等
  • Direct and inverse problems for multi-term time-fractional diffusion equations  [通常講演]
    劉 逸侃
    International Workshop on Inverse Problems and Regularization Theory 2013年09月 口頭発表(一般)
  • Inverse problems for two partial differential equations modeling structure generation and anomalous diffusion  [招待講演]
    劉 逸侃
    偏微分方程式に対する逆問題の数学解析と数値解析 2013年07月 口頭発表(一般)
  • Inverse problems for two evolution equations modeling structure generation and anomalous diffusion  [通常講演]
    劉 逸侃
    Applied Inverse Problem Conference 2013 2013年07月 口頭発表(一般)
  • On a class of multiple hyperbolic systems modeling the phase transformation kinetics  [通常講演]
    劉 逸侃
    The Ninth INS Workshop on Natural Sciences 2013年04月 口頭発表(一般)
  • On a class of multiple hyperbolic systems modeling the phase transformation kinetics  [通常講演]
    劉 逸侃
    逆問題とその周辺分野に関するミニワークショップ 2013年03月 口頭発表(一般)
  • Multiple hyperbolic systems modeling the phase transformation kinetics  [招待講演]
    劉 逸侃
    2013年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Multiple hyperbolic systems modeling the phase transformation kinetics  [招待講演]
    劉 逸侃
    Tsukuba Workshop for Young Mathematicians 2013年02月 口頭発表(招待・特別)
  • The modeling of phase transformation kinetics: Forward and inverse problems  [通常講演]
    劉 逸侃
    Seoul-Tokyo Conference on Elliptic and Parabolic PDEs and Related Topics 2012年12月 ポスター発表
  • Forward and inverse problems concerning the time cone method modeling generation mechanisms  [通常講演]
    劉 逸侃
    International Conference on Inverse Problems and Related Topics 2012 2012年10月 口頭発表(一般)
  • Brainstorming for getting an abstract framework for thinking to tackle social and industrial problems through a combination of geometry and algebra with analysis  [通常講演]
    劉 逸侃
    Study Group Workshop 2012 2012年07月 口頭発表(一般)
  • Forward and inverse problems for hyperbolic systems modelling the nucleation  [招待講演]
    劉 逸侃
    International Workshop on Computational Science and Numerical Analysis 2012年03月 口頭発表(一般)
  • Forward and inverse problems for hyperbolic systems modelling generation of structures  [招待講演]
    劉 逸侃
    2012年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Forward and inverse problems for hyperbolic systems modelling generation of structures  [招待講演]
    劉 逸侃
    2012年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Forward and inverse problems for hyperbolic systems modelling generation of structures  [招待講演]
    劉 逸侃
    2012年02月 公開講演,セミナー,チュートリアル,講習,講義等
  • Forward and inverse problems for hyperbolic systems modelling the generation of structures  [招待講演]
    劉 逸侃
    偏微分方程式の逆問題解析とその周辺分野に関する研究 2012年01月 口頭発表(一般)
  • Forward and inverse problems for some hyperbolic systems modelling generation of structures  [招待講演]
    劉 逸侃
    Conference of the EGDR Control of PDEs 2011年11月 口頭発表(招待・特別)
  • The mathematical modeling for anomalous diffusion in soil  [通常講演]
    劉 逸侃
    Study Group Workshop 2011 2011年08月 口頭発表(一般)

その他活動・業績

受賞

  • 2018年05月 The 10th Annual Meeting on Inverse Problems Excellent Youth Academic Award
  • 2015年03月 東京大学大学院数理科学研究科 研究科長賞
  • 2012年03月 東京大学大学院数理科学研究科 研究科長賞

共同研究・競争的資金等の研究課題

  • 日本学術振興会:科学研究費助成事業 若手研究
    研究期間 : 2020年04月 -2022年03月 
    代表者 : 劉 逸侃
  • 結晶成長と特異拡散の数学解析とその応用
    日本学術振興会:科学研究費助成事業 特別研究員奨励費
    研究期間 : 2016年11月 -2019年03月 
    代表者 : 山本 昌宏, 劉 逸侃, LIU YIKAN
     
    今年度は、非整数階偏微分方程式の順問題および逆問題に対する数学解析を継続し、結晶成長と異常拡散の交差点について研究した。具体的に、異常拡散を表す非整数階偏微分方程式の初期値・境界値問題に関して、次の研究を行った。 1. 順問題:時間微分階数α∈(0,1)かつ解がスカラー値の場合は多くな先行研究があったが、下記の拡張に対する考察を展開した。(a) α∈(1,2)区間に属す場合に対して、坂本-山本による結果を改善し、解の適切性および解析性を証明した。(b) 非整数階反応拡散系を考えるため、ベクトル値の解が満たすカップリング・システムを考え、解の適切性・解析性・漸近挙動を調べた。 2. α∈(0,1)のときの逆問題:(a) 源泉項F(x,t)=f(x)R(x,t)とし、空間成分f(x)を最終時刻の観測データから決定する問題については、解析Fredholm理論によって一意性を示した。(b) 上記と同じ問題で、部分内部領域の観測データによる再構成については、離散化された最適化問題の解の存在性・安定性・収束性を示した。(c) 源泉項および係数を決定する問題に関しては、近年の成果をまとめてレビュー論文を出版した。 3. α∈(1,2]のときの逆問題:順問題の結果を踏まえ、以下の逆問題を考察した。(a) 源泉項が平行移動する場合、ソースの形状を境界全体の近傍の観測で決定する問題について、一意性を証明した。(b) 源泉項がある軌道に沿って移動する場合、有限個の点における観測で軌道を決定する問題について、条件付き安定性を示した。(c) α∈(1,2)の場合、部分境界における一回の観測によって複数の係数を決定する問題については、特殊な境界条件を課すことによって一意性を証明した。

教育活動情報

主要な担当授業

  • 数学総合講義Ⅰ
    開講年度 : 2020年
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 数理モデリング、微分方程式、非線形科学,分岐理論
  • 数理科学演習
    開講年度 : 2020年
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 数値解析・数値計算・シミュレーション・プログラミング・C言語
  • 微分積分学Ⅰ
    開講年度 : 2020年
    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,テイラーの定理
  • 微分積分学Ⅱ
    開講年度 : 2020年
    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,リーマン和,変数変換

大学運営

委員歴

  • 2021年02月 - 現在   偏微分方程式論札幌シンポジウム   プログラム委員
  • 2021年01月 - 現在   「Fractional Calculus and Applied Analysis」編集委員会   Assisting Editor
  • 2019年08月 - 現在   HMMCセミナー   運営委員

学術貢献活動

  • 若手研究集会 「波動・振動・流れの制御と逆問題 -理論と数値計算-」
    期間 : 2021年09月02日 - 2021年09月03日
    役割 : 企画立案・運営等
    種別 : 学会・研究会等
    主催者・責任者 : 伊藤 弘道, 川本 敦史 , 劉 逸侃, 森岡 悠
  • 日本応用数理学会2020年度年会
    期間 : 2020年09月08日 - 2020年09月10日
    役割 : パネル司会・セッションチェア等
    種別 : 学会・研究会等
    主催者・責任者 : 土屋卓也
  • 若手研究集会 「波動・振動・流れの制御と逆問題 -理論と数値計算-」
    期間 : 2019年08月26日 - 2019年08月27日
    役割 : 企画立案・運営等
    種別 : 学会・研究会等
    主催者・責任者 : 伊藤 弘道, 石田 敦英, 劉 逸侃, 森岡 悠
  • Summer School on Applied Inverse Problems and Related Topics
    期間 : 2019年08月07日 - 2019年08月10日
    役割 : 企画立案・運営等
    種別 : 学会・研究会等
    主催者・責任者 : 山本昌宏, 劉逸侃
  • Inverse Problems and Medical Imaging
    期間 : 2018年02月13日 - 2018年02月16日
    役割 : 企画立案・運営等
    種別 : 学会・研究会等
    主催者・責任者 : 星詳子, 劉逸侃, 上坂正晃, 山本昌宏
  • A3 Workshop on Applied Inverse Problems and Related Topics
    期間 : 2017年11月28日 - 2017年11月30日
    役割 : 企画立案・運営等
    種別 : 学会・研究会等
    主催者・責任者 : 山本昌宏, 劉逸侃


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