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Theory of Differential Equations Applied to Biological Pattern Formation--from Analysis to Synthesis

Research Project

Project/Area Number 22244010
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionTohoku University

Principal Investigator

TAKAGI Izumi  東北大学, 理学(系)研究科(研究院), 教授 (40154744)

Co-Investigator(Kenkyū-buntansha) IKEDA Hideo (OKABE Shinya)  富山大学, 大学院理工学研究部, 教授 (60115128)
OGAWA Takayoshi  東北大学, 大学院理学研究科, 教授 (20224107)
NAGASAWA Takeyuki  埼玉大学, 大学院理工学研究科, 教授 (70202223)
YANAGIDA Eiji  東京工業大学, 大学院理工学研究科, 教授 (80174548)
Co-Investigator(Renkei-kenkyūsha) UEYAMA Daishin  明治大学, 理工学部, 准教授 (20304389)
OKABE Shinya  東北大学, 大学院理学研究科, 准教授 (60115128)
NAKASHIMA Kimie  東京海洋大学, 海洋科学部, 准教授 (10318800)
YAMADA Sumio  学習院大学, 理学部, 教授 (90396416)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥46,410,000 (Direct Cost: ¥35,700,000、Indirect Cost: ¥10,710,000)
Fiscal Year 2014: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
Fiscal Year 2013: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2012: ¥10,010,000 (Direct Cost: ¥7,700,000、Indirect Cost: ¥2,310,000)
Fiscal Year 2011: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2010: ¥9,490,000 (Direct Cost: ¥7,300,000、Indirect Cost: ¥2,190,000)
Keywords反応拡散系 / パターン形成 / 不均一媒体 / 非線型楕円型方程式 / 曲面・曲線の変形 / 空間的不均一性 / 自己組織化 / 曲面の変形 / 界面の運動 / 反応拡散方程式系 / 特異摂動解 / 非等方的非一様場 / 幾何学的汎函数 / 活性因子ー抑制因子系 / ヒドラ頭部再生実験 / 運動神経軸索配置 / 楕円形偏微分方程式 / 曲線の変形・運動 / 空間の非均一性 / 放物型偏微分方程式 / ヒドラ頭部再生モデル
Outline of Final Research Achievements

The purpose of this project is to build mathematical theories on reaction-diffusion systems and on the deformation of curves and surfaces, which are necessary to understand, through mathematical models, the dynamic process of morphogenesis in embryonic stages.
In particular, we have succeeded in building a theory on pattern formation in strongly heterogeneous environments, and this will help us devise more biologically realistic models of pattern formation.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (142 results)

All 2015 2014 2013 2012 2011 2010 Other

All Journal Article (42 results) (of which Peer Reviewed: 34 results,  Acknowledgement Compliant: 1 results,  Open Access: 2 results) Presentation (93 results) (of which Invited: 52 results) Book (1 results) Remarks (6 results)

  • [Journal Article] Pattern formation in a diffusion-ODE model with hysteresis2015

    • Author(s)
      A. Marciniak-Czochra, M. Nakayama and I. Takagi
    • Journal Title

      Differential and Integral Equations

      Volume: 印刷中

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A decomposition theorem of the Moebius energy II: Variational formulae and estimates2015

    • Author(s)
      Aya Ishizeki and Takeyuki Nagasawa
    • Journal Title

      Math. Ann.

      Volume: 印刷中 Issue: 1-2 Pages: 617-635

    • DOI

      10.1007/s00208-015-1175-2

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Convergence of equilibrium of gradient flows defined on planar curves2015

    • Author(s)
      M. Novaga and S. Okabe
    • Journal Title

      J. Reine Angew. Math.

      Volume: 印刷中

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extensions of the charged Riemannian Penrose inequality2015

    • Author(s)
      Marcus Khuri, Gilbert Weinstein and Sumio Yamada
    • Journal Title

      Class. Quantum Grav.

      Volume: 32

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local and global aspects of Weil-Petersson geometry2015

    • Author(s)
      Sumio Yamada
    • Journal Title

      Handbook of Teichmuller Theory

      Volume: IV Pages: 43-112

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A decomposition theorem of the Moebius energy I: Decomposition and Moebius invariance2014

    • Author(s)
      Aya Ishizeki and Takeyuki Nagasawa
    • Journal Title

      Kodai Math. J.

      Volume: 37

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-accessible singular homoclinic orbits for semilinear parabolic equation2014

    • Author(s)
      Marek Fila and Eiji Yanagida
    • Journal Title

      Differential and Integral Equations

      Volume: 27 Pages: 563-578

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global unbounded solutions of the Fujita equation in the intermediate range2014

    • Author(s)
      Peter Polacik and Eiji Yanagida
    • Journal Title

      Math. Ann.

      Volume: 360 Pages: 255-266

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics2014

    • Author(s)
      Peter Polacik and Eiji Yanagida
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 46 Pages: 3481-3496

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spontaneous formation of unidirectional path2014

    • Author(s)
      Mayuko Iwamoto, Nobuhiko J. Suematsu, and Daishin Ueyama
    • Journal Title

      Chemical Physics Letters

      Volume: 616-617 Pages: 248-253

    • DOI

      10.1016/j.cplett.2014.10.010

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maze solving using fatty acid chemistry2014

    • Author(s)
      Kohta Suzuno, Daishin Ueyama, Michael Branicki, Rita Toth, Artur Braun and Istvan Lgzi
    • Journal Title

      Langmuir

      Volume: 30 Issue: 31 Pages: 9251-9255

    • DOI

      10.1021/la5018467

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The Advantage of Mucus for Adhesive Locomotion in Gastropods2014

    • Author(s)
      Mayuko Iwamoto, Daishin Ueyama, and Ryo Kobayashi
    • Journal Title

      Journal of Theoretical Biology

      Volume: 353(21) Pages: 133-141

    • DOI

      10.1016/j.jtbi.2014.02.024

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Curve shortening-straightening flow for non-closed planar curves with infinite length2014

    • Author(s)
      M. Novaga and S. Okabe
    • Journal Title

      J. Differential Equations

      Volume: 256 Pages: 1093-1132

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convex bodies in Euclidean and Weil-Petersson geometries.2014

    • Author(s)
      Sumio Yamada
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 142 Issue: 2 Pages: 603-616

    • DOI

      10.1090/s0002-9939-2013-11841-1

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity and asymptotic stability for the Keller-Segel system of degenerate type with critical nonlinearity2013

    • Author(s)
      M. Mizuno, T. Ogawa
    • Journal Title

      J. Math. Sci Univ. Tokyo

      Volume: 20 Pages: 1-59

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity2013

    • Author(s)
      J.-S. Guo, H. Ninomiya, M. Shimojo and E. Yanagida
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 365(5) Pages: 2447-2467

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Behavior of global solutions of the Fujita equation.2013

    • Author(s)
      E. Yanagida
    • Journal Title

      Sugaku Expositions.

      Volume: 26 Pages: 129-147

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Sharp decay estimates of $L^q$-norms for nonnegative Schr\"odinger heat semigroups2013

    • Author(s)
      N. Ioku, K. Ishige and E. Yanagida
    • Journal Title

      Journal of Functional Analysis

      Volume: 264 Pages: 2764-2783

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Analytical investigation of the faster-is-slower effect with a simplified phenomenological model2013

    • Author(s)
      K. Suzuno, A. Tomoeda, and D. Ueyama
    • Journal Title

      Phys. Rev. E

      Volume: 88 Issue: 5 Pages: 0528131-5

    • DOI

      10.1103/physreve.88.052813

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mechanism of spiral formation in heterogeneous discretized excitable media2013

    • Author(s)
      S. Kinoshita, M. Iwamoto, K. Tateishi, N.J. Suematsu, and D. Ueyama
    • Journal Title

      Phys. Rev. E

      Volume: 87 Issue: 6 Pages: 0628151-6

    • DOI

      10.1103/physreve.87.062815

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A global model for impact of elastic shells and its numerical implementation2013

    • Author(s)
      Masaki Kazama, Seiro Omata, Takeyuki Nagasawa, Akira Kikuta, Karel Svadlenka
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 23 Pages: 93-108

    • Related Report
      2013 Annual Research Report
  • [Journal Article] The Funk and Hilbert geometries for spaces of constant curvature.2013

    • Author(s)
      Athanase Papadopoulos, Sumio Yamada
    • Journal Title

      Monatshefte fur Mathematik

      Volume: 172 Issue: 1 Pages: 97-120

    • DOI

      10.1007/s00605-013-0513-2

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A self-organized mesh generator using pattern formation in a reaction-diffusion system2013

    • Author(s)
      Hirofumi Notsu, Daishin Ueyama, Masahiro Yamaguchi
    • Journal Title

      Applied Mathematics Letters

      Volume: Volume 26, Issue 2 Issue: 2 Pages: 201-206

    • DOI

      10.1016/j.aml.2012.08.012

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of the n-dimensional Helfrich flow2013

    • Author(s)
      T.Nagasawa
    • Journal Title

      Springer INdAM Series "Geometric Properties for Parabolic and Elliptic PDE's"

      Volume: 2 Pages: 237-250

    • DOI

      10.1007/978-88-470-2841-8_15

    • ISBN
      9788847028401, 9788847028418
    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact traveling wave solutions of three species competition-diffusion systems2012

    • Author(s)
      C.-C.Chen, L.-C.Hung, M.Mimura and D.Ueyama
    • Journal Title

      DCDS-B

      Volume: 17(8) Issue: 8 Pages: 2653-2669

    • DOI

      10.3934/dcdsb.2012.17.2653

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on a dynamical aspect of shortening-straightening flow for non-closed curves with fixed boundary2012

    • Author(s)
      Shinya Okabe
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B35 Pages: 41-64

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rate of Convergence to Barenblatt Profiles for the Fasr Diffusion Equation2012

    • Author(s)
      M.Fila, J.L.V\'azquez, M.Winkler and E.Yanagida
    • Journal Title

      Arch. Rational Mech. Anal

      Volume: 204(2) Pages: 599-625

    • Related Report
      2012 Annual Research Report
  • [Journal Article] A Complete Solition to an Ambarzumyan Problem on trees2012

    • Author(s)
      C.-K.Law and E.Yanagida
    • Journal Title

      Kodai Math.J

      Volume: 35 Pages: 357-372

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Asymptotic behavior of singular solutions of a semilinear parabolic equation2012

    • Author(s)
      S.Sato and E.Yanagida
    • Journal Title

      Disc. Cont. Dyn. Systems

      Volume: 32 Pages: 4027-4043

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains2012

    • Author(s)
      Fang Lin and Kimie Nakashima
    • Journal Title

      Discrete and Continuous Dyanamical Systems - Series A

      Volume: 32 Pages: 1391-1420

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic distribution of eigenvalues of Hill's equation with integrable potential under periodic condition2011

    • Author(s)
      T.Nagasawa, T.Ohrui
    • Journal Title

      Saitama Mathematical Journal

      Volume: 27 Pages: 1-8

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular backward self-similar solutions of a semilinear parabolic equation2011

    • Author(s)
      S.Sato, E.Yanagida
    • Journal Title

      Discrete Cont.Dynamical Systems-S

      Volume: 4 Pages: 897-906

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Homoclinic and heteroclinic orbits for a semilinear parabolic equation2011

    • Author(s)
      M.Fila, E.Yanagida
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 63 Pages: 561-579

    • NAID

      110008764861

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The existence and convergence of the shortening-straightening flow fornon-closed planar curves with fixed boundary2011

    • Author(s)
      Shinya Okabe
    • Journal Title

      Gakuto International Series, Mathematical Sciences and applications, Internal Symposium on Computational Science 2011

      Volume: 34 Pages: 1-23

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transition layers for a spatially inhomogeneous AUen-Cahn equation in multi-dimensional domains2011

    • Author(s)
      Fang Li, Kimie Nakashima
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 32 Pages: 1391-1420

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the role of basic production terms in an activator-inhibitor system modeling biological pattern formation2011

    • Author(s)
      Kanako Suzuki, Izumi Takagi
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 54 Pages: 237-274

    • NAID

      130000953648

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local uniformization and free boundary regularity of minimal singular surfaces2011

    • Author(s)
      Chikako Mese, Sumio Yamada
    • Journal Title

      Journal of Geometric Analysis

      Volume: 21 Pages: 743-766

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Front Dynamics in heterogeneous diffusive media2010

    • Author(s)
      Ikeda, H., Ei, S,-I.
    • Journal Title

      Pbysica D

      Volume: 239 Pages: 1637-1649

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] End-point maximal regularity and wellposedness of the two dimensional Keller-Segel system in a critical Besov space2010

    • Author(s)
      T.Ogawa, S.Shimizu
    • Journal Title

      Math.Z.

      Volume: 264 Pages: 601-628

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interpolation inequality of logarithmic type in the abstract Besov spaces and application to semilinear evolution equations2010

    • Author(s)
      T.Matsumoto, T.Ogawa
    • Journal Title

      Math.Nachr.

      Volume: 283 Pages: 1-19

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gray-Scottモデルの概要2010

    • Author(s)
      上山大信
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1680 Pages: 1-4

    • Related Report
      2010 Annual Research Report
  • [Journal Article] An indefinite nonlinear diffusion problem in population genetics, I : Existence and limiting profiles2010

    • Author(s)
      Linlin Su, Kimie Nakashima, Wei-Ming Ni
    • Journal Title

      Discrete and Continuous Dynamical Systems-Series A

      Volume: 27 Pages: 617-641

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] A remark on the influence of spatial heterogeneity upon the formation of cell aggregates2015

    • Author(s)
      Izumi Takagi
    • Organizer
      Mini-workshop "Models of directional movement and their analysis"
    • Place of Presentation
      東北大学,数理科学記念館
    • Year and Date
      2015-03-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] 生物の形づくりの数理―Turingが残した課題―2015

    • Author(s)
      高木 泉
    • Organizer
      日本数学会2015年年会,企画特別講演
    • Place of Presentation
      明治大学駿河台キャンパス
    • Year and Date
      2015-03-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Turing's unfinished project2015

    • Author(s)
      Izumi Takagi
    • Organizer
      PDE seminar
    • Place of Presentation
      Center for Partial Differential Equations, East China Normal University, Shanghai, China
    • Year and Date
      2015-03-09 – 2015-03-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Decomposition of the Moebius energy and its consequences2015

    • Author(s)
      Takeyuki Nagasawa
    • Organizer
      The 32nd Kyushu Symposium on Partial Differential Equations
    • Place of Presentation
      九州大学,福岡
    • Year and Date
      2015-01-29
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 点凝集現象を起こす反応拡散系のパターンの制御2015

    • Author(s)
      高木 泉
    • Organizer
      九州関数方程式セミナー
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2015-01-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 空間的不均一性に基づく点凝集パターンの制御2014

    • Author(s)
      高木 泉
    • Organizer
      岡山駅前セミナー:現象を捉える新しい数学的基盤の構築に向けて
    • Place of Presentation
      岡山国際交流センター2階研修室
    • Year and Date
      2014-12-13
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Dynamics of interfaces in the Fisher-KPP equation2014

    • Author(s)
      Eiji Yanagida
    • Organizer
      International Workshop on Nonlinear Partial Differential Equations
    • Place of Presentation
      岡山国際センター,岡山
    • Year and Date
      2014-12-10 – 2014-12-12
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Variational formulae and estimates for decomposed Moebius energies2014

    • Author(s)
      Takeyuki Nagasawa
    • Organizer
      Shapes and other properties of solutions of PDEs
    • Place of Presentation
      京都大学数理解析研究所,京都
    • Year and Date
      2014-11-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Variational characterizations of the static solutions to the Einstein-Maxwell equation2014

    • Author(s)
      Sumio Yamada
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      東北大学,仙台
    • Year and Date
      2014-10-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Control of patterns by way of spatial heterogeneity2014

    • Author(s)
      Izumi Takagi
    • Organizer
      Symposium on Mathematical Approaches to Pattern Formation
    • Place of Presentation
      東北大学,数理科学記念館
    • Year and Date
      2014-10-30
    • Related Report
      2014 Annual Research Report
  • [Presentation] Stability and bifurcation properties of a standing spot solutions in 3-component FitzHugh-Nagumo systems2014

    • Author(s)
      Hideo Ikeda
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      東北大学,仙台
    • Year and Date
      2014-10-29
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Threshold for the global behavior of solution to degenerate Keller-Segel (drift-diffusion) system in between critical exponents2014

    • Author(s)
      Takayoshi Ogawa
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      Tohoku University, Sendai, Japan
    • Year and Date
      2014-10-28 – 2014-10-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Expanding patterns in the Fisher-KPP equation2014

    • Author(s)
      Eiji Yanagida
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      Tohoku University, Sendai
    • Year and Date
      2014-10-28 – 2014-10-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The obstacle problem for a fourth order parabolic equation2014

    • Author(s)
      S. Okabe
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      東北大学,仙台
    • Year and Date
      2014-10-28 – 2014-10-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Decomposition of Moebius energy and Moebius invariance of decomposed energies2014

    • Author(s)
      Takeyuki Nagasawa
    • Organizer
      Mathematical Approaches to Pattern Formation
    • Place of Presentation
      東北大学,仙台
    • Year and Date
      2014-10-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Threshold for the large time behavior of solutions to degenerate drift-diffusion system in between critical exponents2014

    • Author(s)
      Takayoshi Ogawa
    • Organizer
      Mathematics for Fluid Dynamics
    • Place of Presentation
      Universite de Lyon I, Lyon, France
    • Year and Date
      2014-10-20 – 2014-10-23
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 1-dim blooming solutions in a three species Lotka-Volterra system2014

    • Author(s)
      Hideo Ikeda
    • Organizer
      富山解析セミナー2014
    • Place of Presentation
      富山大学,富山
    • Year and Date
      2014-10-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] 四階放物型方程式に対する障害物問題2014

    • Author(s)
      岡部真也
    • Organizer
      日本数学会秋期総合分科会,特別講演
    • Place of Presentation
      広島大学,広島
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Control of patterns by spatial heterogeneity2014

    • Author(s)
      Izumi Takagi
    • Organizer
      HeKKSaGOn Summer School in Goettingen Inference on Pattern Formation: Applications to Biology and Materials Science
    • Place of Presentation
      Goettingen 大学,ドイツ
    • Year and Date
      2014-09-20
    • Related Report
      2014 Annual Research Report
  • [Presentation] On a variational characterization of the exact solutions of the Einstein-Maxwell equation2014

    • Author(s)
      Sumio Yamada
    • Organizer
      MFO Workshop "Analysis, Geometry and Toplogy of Positive Scalar Curvature Metrics
    • Place of Presentation
      Oberwolfach Mathematical Institute, Germany
    • Year and Date
      2014-08-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Role of spatial heterogeneity in pattern formation2014

    • Author(s)
      Izumi Takagi and Hiroko Yamamoto
    • Organizer
      Mini-Symposium "Challenges in mathematical modeling of pattern formation in developmental biology" in JSMB/SMB 2014 meeting
    • Place of Presentation
      大阪コンベンションセンター
    • Year and Date
      2014-07-30
    • Related Report
      2014 Annual Research Report
  • [Presentation] Pattern formation without Turing instability2014

    • Author(s)
      Izumi Takagi
    • Organizer
      Mini-workshop on Modeling, Simulations and Analysis of Pattern Formation
    • Place of Presentation
      東北大学,数理科学記念館
    • Year and Date
      2014-07-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] メビウス・エネルギーの分解定理:幾何学的意味と解析的紅葉2014

    • Author(s)
      長澤壯之
    • Organizer
      東京大学応用解析セミナー
    • Place of Presentation
      東京大学,東京
    • Year and Date
      2014-07-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 3成分FitzHugh-Nagumo 方程式系の2次元スポット解の安定性2014

    • Author(s)
      池田榮雄
    • Organizer
      自己組織化セミナー
    • Place of Presentation
      明治大学,東京
    • Year and Date
      2014-07-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The obstacle problem for the parabolic biharmonic equation2014

    • Author(s)
      S. Okabe
    • Organizer
      京都大学 NLPDE セミナー
    • Place of Presentation
      京都大学,京都
    • Year and Date
      2014-06-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Removable and non-removable singularities in parabolic equations2014

    • Author(s)
      Eiji Yanagida
    • Organizer
      Geometric Aspects of Semilinear Elliptic and Parabolic Equations, Recent Advances and Future Perspectives
    • Place of Presentation
      BIRS, Canada
    • Year and Date
      2014-05-26 – 2014-05-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Existence of non-stabilizing solutions of a semilinear parabolic equation2014

    • Author(s)
      Eiji Yanagida
    • Organizer
      Seminar on PDE
    • Place of Presentation
      Academia Sinica, Taipei, Taiwan
    • Year and Date
      2014-04-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] Convex Bodies in the Euclidean, Spherical, Hyperbolic and Teichmuller Spaces2014

    • Author(s)
      Sumio Yamada
    • Organizer
      Master Class on Finsler Geometry and Applications
    • Place of Presentation
      Galatasaray University, Istanbul, Turkey
    • Year and Date
      2014-04-10 – 2014-04-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Movement of boundary spike solutions of a semilinear parabolic equation2014

    • Author(s)
      高木泉
    • Organizer
      PDE Seminar
    • Place of Presentation
      Center for PDE, East China Normal University, Shanghai, China
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Convergence to equilibrium of gradient flows defined on planar curves2014

    • Author(s)
      Shinya Okabe
    • Organizer
      The 15th Northeastern Symposium on Mathematical Analysis
    • Place of Presentation
      北海道大学 (札幌市)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Asymptotic behavior of curve shortening-straightening flow for planar curves with finite length2014

    • Author(s)
      Shinya Okabe
    • Organizer
      Dynamics and Spacial Functions
    • Place of Presentation
      岩手大学 (盛岡市)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Regularity of solutions to the obstacle problem for the parabolic biharmonic equation2014

    • Author(s)
      Shinya Okabe
    • Organizer
      Joint Research Program on Nonlinear PDE's Universita di Firenze and Tohoku University
    • Place of Presentation
      Universita di Firenze (Firenze, Italy)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Regularity of solutions to the obstacle problem for the parabolic biharmonic equation2014

    • Author(s)
      Shinya Okabe
    • Organizer
      The 6th Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学 (名古屋市)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On Geometry of Weil-Petersson Funk metric2014

    • Author(s)
      山田澄生
    • Organizer
      New Trends in Teichmuller Theory and Mapping Class Groups
    • Place of Presentation
      Oberwolfach数学研究所(MFO),ドイツ
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On Geometry of Weil-Petersson Funk metric2014

    • Author(s)
      山田澄生
    • Organizer
      Geometry and Topology Seminar
    • Place of Presentation
      Strasbourg大学,フランス
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Dynamics of a boundary-spike solution on an invariant manifold to a semilinear parabolic equation2013

    • Author(s)
      高木泉
    • Organizer
      Asian Mathematical Conference
    • Place of Presentation
      Busan, Korea
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Point-condensation phenomenon in a reaction-diffusion system: geometry of domain vs heterogeneity of media2013

    • Author(s)
      高木泉
    • Organizer
      Pacifc Rim Conference on Mathematics 2013
    • Place of Presentation
      Sapporo, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 3成分FitzHugh-Nagumo方程式系のスポット解の不安定性について2013

    • Author(s)
      池田榮雄
    • Organizer
      富山解析セミナー2013
    • Place of Presentation
      富山大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dynamics of front solutions in heterogeneous diffusive media2013

    • Author(s)
      池田榮雄
    • Organizer
      2013 NIMS-KMRS PDE Conference on reaction diffusion equations  for ecology and related problems
    • Place of Presentation
      KAIST(韓国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Threshold for the large time behavior of solutions to degenerate drift-diffusion system in between critical exponents2013

    • Author(s)
      小川卓克
    • Organizer
      金沢大学 理学部 解析セミナー
    • Place of Presentation
      金沢大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Removable and non-removable singularities in parabolic equations2013

    • Author(s)
      柳田英二
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO, Busan, 韓国
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Removable and non-removable singularities in parabolic equations2013

    • Author(s)
      柳田英二
    • Organizer
      Equadiff 2013
    • Place of Presentation
      Prague, Czech Republic
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 単独反応拡散方程式における局在解の収束性2013

    • Author(s)
      柳田英二
    • Organizer
      反応拡散系のパターンダイナミクス
    • Place of Presentation
      富山大学理学部多目的ホール
    • Related Report
      2013 Annual Research Report
  • [Presentation] Construction of solutions to a fourth order parabolic obstacle problem via minimizing movements2013

    • Author(s)
      Shinya Okabe
    • Organizer
      Geometry of solutions of partial differential equations
    • Place of Presentation
      数理解析研究所 (京都市)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On variational characterizations of exact solutions in general relativity2013

    • Author(s)
      山田澄生
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      Sapporo, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of singular solutions for a semilinear parabolic equation2011

    • Author(s)
      Eiji Yanagida
    • Organizer
      Second Italian-Japanese Workshop "Geometric Properties for Elliptic and Parabolic PDE's"
    • Place of Presentation
      Cotrona, Italy
    • Year and Date
      2011-06-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] The existence of shortening-straightening flow for non-closed planar curves with infinite length2011

    • Author(s)
      岡部真也
    • Organizer
      International Symposium on Computational Science 2011
    • Place of Presentation
      金沢大学
    • Year and Date
      2011-02-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Semiclassical and zero relaxation limit for the quantum drift-diffusion system2011

    • Author(s)
      Takayoshi Ogawa
    • Organizer
      19tb Workshop on Differential Equations and its Applications
    • Place of Presentation
      National Cheng Kung University, Tainan, Taiwan
    • Year and Date
      2011-01-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dynamics of traveling fronts in some heterogeneous diffusive media2011

    • Author(s)
      Ikeda, H.
    • Organizer
      19th Workshop on Differential Equations and its Applications
    • Place of Presentation
      National Cheng Kung University, Tainan, Taiwan
    • Year and Date
      2011-01-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Shortening-straightening flowによって支配される無限の長さをもつ平面曲線の挙動2010

    • Author(s)
      岡部真也
    • Organizer
      関数解析と実解析による微分方程式
    • Place of Presentation
      かんぽの宿松島
    • Year and Date
      2010-12-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Mathematical model or Liesegang type precipitation2010

    • Author(s)
      Daishin Ueyama
    • Organizer
      Inorganic Nanowires : Syntheses and Growth Mechanisms, The International Chemical Congress of Pacific Basin Societies
    • Place of Presentation
      Hawaii Convention Center 304A, Honolulu, Hawai, USA
    • Year and Date
      2010-12-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Uniformization of minimal singlular surfaces2010

    • Author(s)
      Sumio Yamada
    • Organizer
      Workshop on Teichmuller Theory
    • Place of Presentation
      Oberwolfach数学研究所,ドイツ
    • Year and Date
      2010-12-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] "Where's the peak?":極大点の在処を求めて2010

    • Author(s)
      高木泉
    • Organizer
      数学の展開…諸分野との連携を探る
    • Place of Presentation
      東北大学理学部
    • Year and Date
      2010-11-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] The n-dimensional Helfrich flow2010

    • Author(s)
      Takeyuki Nagasawa
    • Organizer
      International Workshop on PDE "Concentration and Related Topics in Nonlinear Problems"
    • Place of Presentation
      東北大学理学部
    • Year and Date
      2010-11-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Location of layers for a spatially inhomogeneous balanced bistable equation2010

    • Author(s)
      Kimie Nakashima
    • Organizer
      非線形解析と可積分系の数理
    • Place of Presentation
      龍谷大学
    • Year and Date
      2010-11-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Global structure of traveling wave solutions in bistable reaction-diffusion systems2010

    • Author(s)
      Ikeda, H.
    • Organizer
      散逸系の数理--解構造と大域挙動--structures of Attractors in Dissipative Systems
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-11-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Attractors of an activator-inhibitor system in homogeneous media and an application2010

    • Author(s)
      Izumi Takagi
    • Organizer
      Dissipative Systems…Attractors and Global Behavior…
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-11-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] A mathematical model of Liesegang type precipitation2010

    • Author(s)
      Daishin Ueyama
    • Organizer
      Mini-Workshop on Modeling, Simulations and Analysis of Biological Pattern Formation
    • Place of Presentation
      ハーネル仙台
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] An application of the self-organizing mechanism in the reaction-diffusion systems2010

    • Author(s)
      Daishin Ueyama
    • Organizer
      International Workshop on Pattern Formation in Chemical and Biological Systems
    • Place of Presentation
      Eotvos University, Budapest, Hungary
    • Year and Date
      2010-10-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] One of the applications of the self-replicating mechanism in some reaction-diffusion systems2010

    • Author(s)
      Daishin Ueyama
    • Organizer
      Reaction-Diffusion Systems : Experiments, Modeling and Analysisi
    • Place of Presentation
      Paris-Sud 11, Orsay, France
    • Year and Date
      2010-10-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] The motion of non-closed planar curves governed by shortening-straight ening flow2010

    • Author(s)
      岡部真也
    • Organizer
      現象の数理解析に向けた非線形発展方程式とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] n-dimensional Helfrich flow2010

    • Author(s)
      長澤壯之
    • Organizer
      The Sixth "Topics in Nonlinear Problems"
    • Place of Presentation
      山口大学理学部
    • Year and Date
      2010-09-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Breakdown of pattern formation in activator-inhibitor systems and unfolding of a singular equilibrium2010

    • Author(s)
      Izumi Takagi
    • Organizer
      Partial Differential Equations in Mathematical Biology
    • Place of Presentation
      Bedlewo Conference Center,ポーランド
    • Year and Date
      2010-09-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 非一様拡散場に現れる様々なダイナミクス~大域的解構造に向けて~2010

    • Author(s)
      池田榮雄
    • Organizer
      第4回応用数理研究会
    • Place of Presentation
      ニューサンピア敦賀
    • Year and Date
      2010-08-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Collapse of patterns in activator-inhibitor systems2010

    • Author(s)
      I.Takagi
    • Organizer
      Fourth International Conference on Recent Advances in Applied Dynamical Systems
    • Place of Presentation
      浙江師範大学,金華,中国
    • Year and Date
      2010-06-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains2010

    • Author(s)
      Kimie Nakashima
    • Organizer
      Nonlinear Evolution PDEs and their Equilibrium States
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-06-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] Gradient flow for the Helfrich variational problem2010

    • Author(s)
      長澤壯之
    • Organizer
      New Trends of Variational Problems
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-06-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Traveling front dynamics in some heterogeneous diffusive media2010

    • Author(s)
      Ikeda, H.
    • Organizer
      The 8^<th> AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Dresden University of Technology, Germany
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] The critical case of drift-diffusion system of degenerate type2010

    • Author(s)
      Takayoshi Ogawa
    • Organizer
      8^<th> AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Dresden University of Technology, Germany
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] From metaphors to models, or top-down vs. bottom-up approaches

    • Author(s)
      I. Takagi
    • Organizer
      2012 Summer School of the HeKKSaGOn Consortium "Crossing Borders: Unraveling Principles of Life with quantitative Tools"
    • Place of Presentation
      Heidelberg, 独国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Dynamics of traveling fronts in some heterogeneous diffusive media

    • Author(s)
      H.Ikeda
    • Organizer
      9th AIMS International Conference on Dynamical Systems
    • Place of Presentation
      Florida, 米国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Front dynamics in heterogeneous media

    • Author(s)
      H.Ikeda
    • Organizer
      Turing Symposium on Morphogenesis,Mathematical approaches sixty years after Alan Turing
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 3成分反応拡散系の空間2次元パターン

    • Author(s)
      池田榮雄
    • Organizer
      富山解析セミナー2012
    • Place of Presentation
      富山大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 3成分FitzHugh-Nagumo方程式系の局在パターン

    • Author(s)
      池田榮雄
    • Organizer
      KSU非線型解析セミナー
    • Place of Presentation
      京都産業大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 3成分FitzHugh-Nagumo方程式系の空間1次元、および2次元での局在パターン

    • Author(s)
      池田榮雄
    • Organizer
      北大MM倶楽部セミナー
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Blow-up criterion for the compressible Navier-Stokes-Poisson system

    • Author(s)
      T.Ogawa
    • Organizer
      5th Euro-Japanese Workshop on Blow-up in CIRM
    • Place of Presentation
      Marseille-Luminy, 仏国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Existence of solution to the compressible Navier-Stokes-Poisson system and the relation with the drift-diffusion system

    • Author(s)
      T.Ogawa
    • Organizer
      MathFlows 2012 in Porquerolles
    • Place of Presentation
      Porquerolles, 仏国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Local existence result for the compressible Navier-Stokes-Poisson system in a critical case

    • Author(s)
      T.Ogawa
    • Organizer
      CAU-Kyoto University Joint Workshop on Nonlinear PDEs
    • Place of Presentation
      Seoul,韓国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Global existence and blow up for a weak solution to degenerate drift-diffusion system between two critical cases

    • Author(s)
      T.Ogawa
    • Organizer
      PDE seminar
    • Place of Presentation
      Sydney,オーストラリア
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Longtime existence of shortening-straightening flow for non-closed planar curves with infinite lenght

    • Author(s)
      Shinya Okabe
    • Organizer
      The 9th AIMS Conference on Dynamical System-Differential Equations and Applications
    • Place of Presentation
      Florida, 米国
    • Related Report
      2012 Annual Research Report
  • [Presentation] Existence and convergence of solutions to the shortening-straightening flow for non-closed planar curves with infinite length

    • Author(s)
      Shinya Okabe
    • Organizer
      Calculus of Variations and Geometric Measure Theory
    • Place of Presentation
      Pisa, イタリア
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] The variational problem for a certain space-time functional defined on planar closed curves

    • Author(s)
      Shinya Okabe
    • Organizer
      Differential Equations and Applications
    • Place of Presentation
      Padova,イタリア
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic Behavior of Singular Solutions for a Semilinear Parabolic Equation

    • Author(s)
      柳田英二
    • Organizer
      9th AIMS International Conference on Dynamical Systems
    • Place of Presentation
      Orlando,米国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Convergence to Barenblatt Profiles for the Fast Diffusion Equation

    • Author(s)
      柳田英二
    • Organizer
      Second Sino-Chilean Conference on Nonlinear Partial Differential Equations
    • Place of Presentation
      Santiago,チリ
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Diffusion-induced phenomena in nonlinear systems

    • Author(s)
      柳田英二
    • Organizer
      Turing Symposium on Morphogenesis,Mathematical approaches sixty years after Alan Turing
    • Place of Presentation
      仙台
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of singular solutions for a semilinear parabolic equation

    • Author(s)
      柳田英二
    • Organizer
      IMA Annual Programs: Infinite Dimensional and Stochastic Dynamical Systems and Their Applications, Workshop:Dynamical Systems in Studies of Partial Differential Equations
    • Place of Presentation
      Minneapolis, 米国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Non-accessible singular homoclinic orbits for a semilinear parabolic equation

    • Author(s)
      柳田英二
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      Zurich,スイス
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Singular Solutions of a Seimilinear Parabolic equation

    • Author(s)
      柳田英二
    • Organizer
      UK-Japan Winter School--Nonlinear Analysis
    • Place of Presentation
      London,英国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] タイヒミュラー空間のWeil-Petersson凸幾何学

    • Author(s)
      山田澄生
    • Organizer
      幾何学シンポシウム
    • Place of Presentation
      福岡
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Onthe Weil-Petersson convex geometry of Teichmuller spaces

    • Author(s)
      Sumio Yamada
    • Organizer
      Geometry Seminar
    • Place of Presentation
      Lausanne,仏国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Convex geometry on constant curvature spaces

    • Author(s)
      Sumio Yamada
    • Organizer
      Tsinghua-Sanya International Mathematics Forum
    • Place of Presentation
      三亞,中国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On variational formulations of the Funk and Barbilian metrics

    • Author(s)
      Sumio Yamada
    • Organizer
      Trimester thematic program "Teichmuller Theory"
    • Place of Presentation
      Wien,オーストリア
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Effect of the heterogeneity on the concentration point in the ground-state solution of a reaction-diffusion equation

    • Author(s)
      H. Yamamoto (代表者), I. Takagi
    • Organizer
      American Mathematical Society Southeastern Section Meeting
    • Place of Presentation
      New Orleans 米国
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Book] 非線型発展方程式の実解析的手法2013

    • Author(s)
      小川卓克
    • Total Pages
      420
    • Publisher
      シュプリンガージャパン社
    • Related Report
      2012 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

    • Related Report
      2014 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

      http://morphos.jp/

    • Related Report
      2014 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

    • Related Report
      2013 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

    • Related Report
      2012 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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