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Pattern dynamics of reaction-diffusion systems and free boundary problems

Research Project

Project/Area Number 26287024
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionMeiji University

Principal Investigator

Ninomiya Hirokazu  明治大学, 総合数理学部, 専任教授 (90251610)

Co-Investigator(Kenkyū-buntansha) 飯田 雅人  宮崎大学, 工学部, 教授 (00242264)
矢崎 成俊  明治大学, 理工学部, 専任教授 (00323874)
高坂 良史  神戸大学, 海事科学研究科, 准教授 (00360967)
谷口 雅治  岡山大学, 異分野基礎科学研究所, 教授 (30260623)
三竹 大寿  広島大学, 工学研究科, 准教授 (90631979)
Co-Investigator(Renkei-kenkyūsha) MONOBE Harunori  岡山大学, 異分野基礎科学研究所, 准教授 (20635809)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2017: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Keywordsパターン形成 / 反応拡散系 / 自由境界問題 / 特異極限法 / 進行波解 / スパイラル / パターンダイナミクス / 特異極限 / 応用数学 / 全域解 / 特異極限問題 / 国際研究者交流(台湾,フランス,アメリカ)
Outline of Final Research Achievements

To study the spatial patterns of solutions of partial differential equations, such as reaction-diffusion systems, we introduce a reaction-interface system, which consists of the interface equation and an equation in the whole space. This is derived as a singular limit of some reaction-diffusion systems. We studied the multidimensional traveling wave solution and the pulse dynamics of the reaction-interface system. Moreover, for the curvature flow with the anisotropic external force, we study the influence of the anisotropy to the compact traveling wave solutions. We also introduce the layered system to analyze the spatial profiles of solutions in multidimensional space.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (88 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (42 results) (of which Int'l Joint Research: 12 results,  Peer Reviewed: 40 results,  Acknowledgement Compliant: 15 results,  Open Access: 10 results) Presentation (38 results) (of which Int'l Joint Research: 22 results,  Invited: 37 results) Book (4 results) Funded Workshop (1 results)

  • [Int'l Joint Research] 国立台南大学/国立台湾大学/淡江大学(台湾)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] National Taiwan University/Tamkang University/National Nainan University(台湾)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] National Taiwan University/Tamkan University/National Tainan University(台湾)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Entire solutions originating from monotone fronts to the Allen-Cahn equation2018

    • Author(s)
      Y.-Y. Chen, J.-S. Guo, H. Ninomiya and C.-H. Yao
    • Journal Title

      Physica D

      Volume: - Pages: 1-19

    • DOI

      10.1016/j.physd.2018.04.003

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On uniqueness sets of additive eigenvalue problems and applications2018

    • Author(s)
      H. Mitake, H. V. Tran
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: -

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Weak KAM theory for discount Hamilton-Jacobi equations and its application2018

    • Author(s)
      H. Mitake, K. Soga
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: -

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Traveling wave solutions with convex domains for a free boundary problem2017

    • Author(s)
      H. Monobe and H. Ninomiya
    • Journal Title

      Discrete and Continuous Dynamical Systems. Ser. A

      Volume: Volume 37, Issue 2 Issue: 2 Pages: 905-914

    • DOI

      10.3934/dcds.2017037

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence of rotating spots with spatially dependent feedback in the plane in a wave front interaction model2017

    • Author(s)
      Y.-Y. Chen, J.-S. Guo and H. Ninomiya
    • Journal Title

      Journal of Dynamics and Differential Equations

      Volume: 29 Issue: 2 Pages: 465-483

    • DOI

      10.1007/s10884-016-9541-7

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Traveling curved waves in two dimensional excitable media2017

    • Author(s)
      H. Ninomiya and C.-H. Wu
    • Journal Title

      SIAM J. Mathematical Analysis

      Volume: 49 Issue: 2 Pages: 777-817

    • DOI

      10.1137/16m1064040

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Reaction, diffusion and non-local interaction2017

    • Author(s)
      H. Ninomiya, Y. Tanaka and H. Yamamoto
    • Journal Title

      Journal of Mathematical Biology

      Volume: 75 Issue: 5 Pages: 1203-1233

    • DOI

      10.1007/s00285-017-1113-x

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Vanishing, moving and immovable interfaces in fast reaction limits2017

    • Author(s)
      M. Iida, H. Monobe, H. Murakawa and H. Ninomiya
    • Journal Title

      Journal of Differential Equations

      Volume: 印刷中 Issue: 5 Pages: 2715-2735

    • DOI

      10.1016/j.jde.2017.04.009

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Mathematical approach to nonlocal interactions using a reaction-diffusion system2017

    • Author(s)
      Y. Tanaka, H. Yamamoto, and H. Ninomiya
    • Journal Title

      Development, Growth & Differentiation

      Volume: - Issue: 5 Pages: 388-395

    • DOI

      10.1111/dgd.12354

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the criteria for the stability of unduloids2017

    • Author(s)
      Y. Kohsaka
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B63 Pages: 169-194

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Method of fundamental solutions with weighted average condition and dummy points2017

    • Author(s)
      K. Sakakibara and S. Yazaki
    • Journal Title

      JSIAM Letters

      Volume: 9 Issue: 0 Pages: 41-44

    • DOI

      10.14495/jsiaml.9.41

    • NAID

      130006900325

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Instability of a free boundary in a Hele-Shaw cell with sink/source and its parameter dependence2017

    • Author(s)
      H. Tani and S. Yazaki
    • Journal Title

      JSIAM Letters

      Volume: 9 Issue: 0 Pages: 37-40

    • DOI

      10.14495/jsiaml.9.37

    • NAID

      130006900379

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 自己駆動粒子モデルにおける「群れ」の特徴付け2017

    • Author(s)
      谷村優太,友枝明保,木下修一,矢崎成俊
    • Journal Title

      武蔵野大学数理工学センター紀要

      Volume: 2 Pages: 20-38

    • NAID

      120006307310

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Method of fundamental solutions with weighted average condition and dummy points2017

    • Author(s)
      K. Sakakibara and S. Yazaki
    • Journal Title

      Applied Mathematics Letters

      Volume: 印刷中 Pages: 16-21

    • DOI

      10.1016/j.aml.2017.04.018

    • NAID

      130006900325

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Instability of a free boundary in a Hele-Shaw cell with sink/source and its parameter dependence2017

    • Author(s)
      H. Tani and S. Yazaki
    • Journal Title

      JSIAM Letters

      Volume: 印刷中

    • NAID

      130006900379

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Selection problems for a discount degenerate viscous Hamilton--Jacobi equation2017

    • Author(s)
      H. Mitake, H. V. Tran
    • Journal Title

      Adv. Math.

      Volume: 306 Pages: 684-703

    • DOI

      10.1016/j.aim.2016.10.032

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus2017

    • Author(s)
      H. Ishii, H. Mitake, H. V. Tran
    • Journal Title

      Journal de Mathematiques Pures et Appliquees

      Volume: 印刷中 Issue: 2 Pages: 125-149

    • DOI

      10.1016/j.matpur.2016.10.013

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems2017

    • Author(s)
      H. Ishii, H. Mitake, H. V. Tran
    • Journal Title

      Journal de Mathematiques Pures et Appliquees

      Volume: 印刷中 Issue: 3 Pages: 261-305

    • DOI

      10.1016/j.matpur.2016.11.002

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A reaction diffusion model for understanding phyllotactic formation2016

    • Author(s)
      Y. Tanaka, M. Mimura and H. Ninomiya
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 33 Issue: 1 Pages: 183-205

    • DOI

      10.1007/s13160-015-0202-8

    • NAID

      210000175348

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Convex compact sets in $\mathbb{R}^{\scriptscriptstyle N-1}$ give traveling fronts of cooperation-diffusion systems in $\mathbb{R}^{\scriptscriptstyle N}$2016

    • Author(s)
      Masaharu Taniguchi
    • Journal Title

      Journal of Differential Equations

      Volume: 260 Issue: 5 Pages: 4301-4338

    • DOI

      10.1016/j.jde.2015.11.010

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation2016

    • Author(s)
      Y. Kohsaka
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 176 Pages: 121-148

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms2016

    • Author(s)
      Y. Giga, H. Mitake and H. V. Tran
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 48 Issue: 5 Pages: 3515-3546

    • DOI

      10.1137/15m1052755

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Traveling wave solutions with convex domains for a free boundary problem2016

    • Author(s)
      H. Monobe and H. Ninomiya
    • Journal Title

      Discrete and continuous dynamical systems. Ser. A

      Volume: 印刷中

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A Lagrangian approach to weakly coupled Hamilton-Jacobi systems2016

    • Author(s)
      H. Mitake, A. Siconolfi, H. V. Tran, N. Yamada,
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 48 Issue: 2 Pages: 821-846

    • DOI

      10.1137/15m1010841

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the existence of two stationary solutions for a free boundary problem describing cell motility2016

    • Author(s)
      H. Monobe
    • Journal Title

      Tamkang Journal of Mathematics

      Volume: 47 Issue: 1

    • DOI

      10.5556/j.tkjm.47.2016.1889

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling spots on multi-dimensional excitable media2015

    • Author(s)
      Y.-Y. Chen, H. Ninomiya and R. Taguchi
    • Journal Title

      Journal of Elliptic and Parabolic Equations

      Volume: 1 Pages: 281-305

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] An (N-1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen-Cahn equation2015

    • Author(s)
      Masaharu Taniguchi
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 47 Issue: 1 Pages: 455-476

    • DOI

      10.1137/130945041

    • NAID

      120005657667

    • Related Report
      2015 Annual Research Report 2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Exact solution for dislocation bowing and a posteriori numerical technique for dislocation touching-splitting2015

    • Author(s)
      P. Paus and S. Yazaki
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 57-60

    • DOI

      10.14495/jsiaml.7.57

    • NAID

      130005097358

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 
Towards modelling spiral motion of open plane curves2015

    • Author(s)
      K. Osaki, H. Satoh and S. Yazaki
    • Journal Title

      
Discrete and Continuous Dynamical Systems - Series S

      Volume: 8

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 
A numerical scheme for the Hele-Shaw flow with a time-dependent gap by a curvature adjusted method2015

    • Author(s)
      S. Yazaki
    • Journal Title

      

Nonlinear Dynamics in Partial Differential Equations, Adv. Stud. Pure Math.

      Volume: 64

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large-time behavior for obstacle problems for degenerate viscous Hamilton-Jacobi equations2015

    • Author(s)
      H. Mitake, H. V. Tran
    • Journal Title

      Calc. Var. Partial Differential Equations.

      Volume: 54 Issue: 2 Pages: 2039-2058

    • DOI

      10.1007/s00526-015-0855-9

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Existence for stationary mean field games with quadratic Hamiltonians with congestion2015

    • Author(s)
      D. Gomes, H. Mitake
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl.

      Volume: 22 Issue: 6 Pages: 1897-1910

    • DOI

      10.1007/s00030-015-0349-7

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Behavior of radially symmetric solutions for a free boundary problem related to cell motility,2015

    • Author(s)
      H. Monobe
    • Journal Title

      Discrete and Continuous Dynamical Systems Series S

      Volume: 8 Issue: 5 Pages: 989-997

    • DOI

      10.3934/dcdss.2015.8.989

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new method for large time behavior of degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians2015

    • Author(s)
      F. Cagnetti, D. A. Gomes, H. Mitake and H. V. Tran
    • Journal Title

      Ann. Inst. H. Poincare Anal. Non Lineaire

      Volume: 32 Pages: 183-200

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems2014

    • Author(s)
      Y.-Y. Chen, Y. Kohsaka and H. Ninomiya
    • Journal Title

      Discrete and continuous dynamical systems. Ser. B

      Volume: 19 Issue: 3 Pages: 697-714

    • DOI

      10.3934/dcdsb.2014.19.697

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple existence of traveling waves of a free boundary problem describing cell motility2014

    • Author(s)
      H. Monobe and H. Ninomiya:
    • Journal Title

      Discrete and continuous dynamical systems. Ser. B

      Volume: 19 Issue: 3 Pages: 789-799

    • DOI

      10.3934/dcdsb.2014.19.789

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 反応拡散近似とその周辺2014

    • Author(s)
      飯田雅人, 二宮広和
    • Journal Title

      数学

      Volume: 66 Pages: 225-248

    • NAID

      130005689994

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of the Laplace-Beltrami operator on a large spherical cap under the Robin problem2014

    • Author(s)
      Y. Kabeya, T. Kawakami, A. Kosaka and H. Ninomiya
    • Journal Title

      Kodai Mathematical Journal

      Volume: 37 Pages: 620-645

    • NAID

      130004705916

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular Neumann problems and large-time behavior of solutions of non-coercive Hamilton--Jacobi equations2014

    • Author(s)
      Y. Giga, Q. Liu and H. Mitake
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 366 Pages: 1905-1941

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A dynamical approach to the large-time behavior of solutions to weakly coupled systems of Hamilton--Jacobi equations2014

    • Author(s)
      H. Mitake and H. V. Tran
    • Journal Title

      J. Math. Pures Appl.

      Volume: 9 Pages: 76-93

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates2014

    • Author(s)
      H. Mitake and H. V. Tran
    • Journal Title

      Arch. Ration. Mech. Anal.

      Volume: 211 Pages: 733-769

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion2013

    • Author(s)
      T. Ishiwata and S. Yazaki
    • Journal Title

      Discrete Contin. Dynam. Systems A

      Volume: 34, Issue 5 Issue: 5 Pages: 2069-2090

    • DOI

      10.3934/dcds.2014.34.2069

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Dynamics of solutions of interface-reaction systems2018

    • Author(s)
      H. Ninomiya
    • Organizer
      The 3rd International Conference on Dynamics of Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamics of interface-reaction equations2018

    • Author(s)
      H. Ninomiya
    • Organizer
      International Conference on Nonlinear Analysis and its Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 反応拡散方程式の進行波解と全域解2018

    • Author(s)
      二宮広和
    • Organizer
      日本数学会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Traveling waves of curvature flows with anisotropic external forces2017

    • Author(s)
      H. Ninomiya
    • Organizer
      Mathematical Analysis on Nonlinear PDEs
    • Place of Presentation
      東北大学,仙台
    • Year and Date
      2017-01-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Reaction-diffusion approximations of non-local evolutionary equation and wave equation2017

    • Author(s)
      H. Ninomiya
    • Organizer
      International Conference on Elliptic and Parabolic Problems
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamics of waves in excitable media2017

    • Author(s)
      H. Ninomiya
    • Organizer
      日本数理生物学会
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamics of waves in excitable media2017

    • Author(s)
      H. Ninomiya
    • Organizer
      The 3rd conference on Differential Geometry and Differential equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An (N-1)-dimensional convex compact set gives an N-dimensional traveling front2017

    • Author(s)
      M. Taniguchi
    • Organizer
      Equadiff2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Derivation of multi-layered interface system and its application2017

    • Author(s)
      H. Mitake
    • Organizer
      Nonlinear PDE for Future Applications -Optimal Control and PDE
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence of asymptotic speed for level set equations with source term,2017

    • Author(s)
      H. Mitake
    • Organizer
      発展方程式の理論と非線形現象の数学解析
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability and bifurcation diagram of the steady states for the surface diffusion equation2017

    • Author(s)
      Y. Kohsaka
    • Organizer
      Viscosity solution approach to asymptotic problems in front propagation, dynamical system and related topics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 界面現象に現れる移動境界の追跡法2017

    • Author(s)
      矢崎成俊
    • Organizer
      日本数学会2016年度年会(応用数学分科会)
    • Place of Presentation
      首都大学(東京)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] How to track the moving boundary arising in interfacial phenomena2017

    • Author(s)
      S. Yazaki
    • Organizer
      Reaction-diffusion system, theory and applications
    • Place of Presentation
      明治大学(東京)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] An (N-1)-dimensional convex compact set gives an N-dimensional traveling front2016

    • Author(s)
      Masaharu Taniguchi
    • Organizer
      International Conference for the 70th Anniversary of Korean Mathematical Society
    • Place of Presentation
      Seoul National University, 韓国
    • Year and Date
      2016-10-20
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Obstacle-induced spiral in two-dimensional excitable media2016

    • Author(s)
      H. Ninomiya
    • Organizer
      ミクロな振る舞いと集団的パターン形成に係る階層的構造の解明
    • Place of Presentation
      数理解析研究所,京都
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Pattern formation through non-local interactions2016

    • Author(s)
      H. Ninomiya
    • Organizer
      The 2016 (26th) annual meeting of the Japanese Society for Mathematical Biology
    • Place of Presentation
      九州大学,福岡
    • Year and Date
      2016-09-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Area-preserving crystalline curvature flow equation and analysis of vapor figure in ice block2016

    • Author(s)
      S. Yazaki
    • Organizer
      Czech-Japanese-Polish seminar in applied mathematics 2016
    • Place of Presentation
      AGH University of Science and Technology (Krakow, Poland)
    • Year and Date
      2016-09-05
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Layered Interface Systems and its Dynamics2016

    • Author(s)
      H. Ninomiya
    • Organizer
      11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications,
    • Place of Presentation
      Orlando, USA
    • Year and Date
      2016-07-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An (N-1)-dimensional convex compact set gives an N-dimensional traveling front2016

    • Author(s)
      M. Taniguchi
    • Organizer
      11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, USA
    • Year and Date
      2016-07-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On rate of the convergence for the discount vanishing problem2016

    • Author(s)
      H. Mitake
    • Organizer
      11th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, USA
    • Year and Date
      2016-07-01
    • Related Report
      2016 Annual Research Report
  • [Presentation] Obstacle-induced spiral formation in excitable media and ventricular fibrillation2016

    • Author(s)
      H. Ninomiya
    • Organizer
      ALGORITMY 2016, Conference on Scientific Computing
    • Place of Presentation
      Vysoke Tatry, Podbanske
    • Year and Date
      2016-03-13
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A direct approach to image segmentation2016

    • Author(s)
      S. Yazaki
    • Organizer
      ALGORITMY 2016, Conference on Scientific Computing
    • Place of Presentation
      Vysoke Tatry, Podbanske
    • Year and Date
      2016-03-13
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of Delaunay surfaces as the steady states for the surface diffusion equation2015

    • Author(s)
      高坂良史
    • Organizer
      Geometric aspects on capillary problems and related topics
    • Place of Presentation
      Granada (スペイン)
    • Year and Date
      2015-12-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 興奮場の特異極限問題と不整脈への応用,2015

    • Author(s)
      二宮広和
    • Organizer
      北大PDEセミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2015-11-30
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms2015

    • Author(s)
      H. Mitake
    • Organizer
      Developments in the theory of Homogenization,
    • Place of Presentation
      Banff research station (Canada)
    • Year and Date
      2015-07-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Analysis of stability of the CMC surfaces via the surface diffusion equation2015

    • Author(s)
      高坂良史
    • Organizer
      Summer School on multiscale and geometric analysis
    • Place of Presentation
      北海道大学
    • Year and Date
      2015-07-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A generalization of discounted approximation and application to non-convex Hamilton--Jacobi equations2015

    • Author(s)
      H. Mitake
    • Organizer
      The Hamilton-Jacobi Equation: At the crossroads of PDE, dynamical systems and geometry,
    • Place of Presentation
      Cortona (Italy)
    • Year and Date
      2015-07-23
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] (N-1)次元空間におけるコンパクトな凸図形の与えるN次元進行波2015

    • Author(s)
      谷口雅治
    • Organizer
      広島大学理学部数学教室談話会
    • Place of Presentation
      広島大学
    • Year and Date
      2015-06-30
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the criteria for the stability of unduloids2015

    • Author(s)
      高坂良史
    • Organizer
      保存則をもつ偏微分方程式に対する 解の正則性・特異性の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-06-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the criteria for the stability of the axisymmetric CMC2015

    • Author(s)
      高坂良史
    • Organizer
      4th Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE’s
    • Place of Presentation
      Palinuro, Italy
    • Year and Date
      2015-05-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stochastic Mather measure and discounted approximation2015

    • Author(s)
      H. Mitake
    • Organizer
      Computational, Applied Mathematics and PDE seminar,
    • Place of Presentation
      Univ. Chicago, U.S.A.
    • Year and Date
      2015-04-01
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 退化粘性ハミルトン・ヤコビ方程式の漸近解析: 長時間挙動と選択問題2015

    • Author(s)
      三竹 大寿
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式と平均曲率一定曲面2015

    • Author(s)
      高坂良史
    • Organizer
      RIMS研究集会「パターン形成と界面ダイナミクスの数理」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-01-07 – 2015-01-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Dynamics of a free boundary problem arising from excitable systems2014

    • Author(s)
      H. Ninomiya
    • Organizer
      Sixth Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      東京工業大学
    • Year and Date
      2014-09-01 – 2014-09-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Traveling spots and obstacle-induced spirals in an excitable medium2014

    • Author(s)
      H. Ninomiya
    • Organizer
      The 10th AIMS International Conference on Dynamical Systems, Differential Equations, and Applications
    • Place of Presentation
      Universidad Autónoma de Madrid, Spain
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式に対する定常解の安定性解析2014

    • Author(s)
      高坂良史
    • Organizer
      信州大学偏微分方程式研究集会
    • Place of Presentation
      信州大学
    • Year and Date
      2014-06-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Traveling spots and obstacle-induced spirals in an excitable medium2014

    • Author(s)
      H. Ninomiya
    • Organizer
      BIRS Workshop 14w5017, Geometric Aspects of Semilinear Elliptic and Parabolic Equations: Recent Advances and Future Perspectives
    • Place of Presentation
      Banff International Research Station, Canada
    • Year and Date
      2014-05-25 – 2014-05-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Convex compact sets in R^{N-1} give traveling fronts in R^N in cooperative diffusion systems2014

    • Author(s)
      M. Taniguchi
    • Organizer
      BIRS Workshop 14w5017, Geometric Aspects of Semilinear Elliptic and Parabolic Equations: Recent Advances and Future Perspectives
    • Place of Presentation
      Banff International Research Station, Canada
    • Year and Date
      2014-05-25 – 2014-05-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Book] Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampere Equations2017

    • Author(s)
      N. Q. Le and H. Mitake and H. V. Tran
    • Total Pages
      240
    • Publisher
      Springer
    • ISBN
      3319542079
    • Related Report
      2017 Annual Research Report
  • [Book] 界面現象と曲線の微積分2016

    • Author(s)
      矢崎成俊
    • Total Pages
      221
    • Publisher
      共立出版
    • Related Report
      2016 Annual Research Report
  • [Book] 実験数学読本:真剣に遊ぶ数理実験から大学数学へ,2016

    • Author(s)
      矢崎成俊
    • Total Pages
      248
    • Publisher
      日本評論社
    • Related Report
      2016 Annual Research Report
  • [Book] 侵入・伝播と拡散方程式2014

    • Author(s)
      二宮広和
    • Total Pages
      185
    • Publisher
      共立出版
    • Related Report
      2014 Annual Research Report
  • [Funded Workshop] Okayama Workshop on Partial Differential Equations2016

    • Place of Presentation
      岡山大学理学部2号館
    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-22  

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