Research on the stability and asymptotic shapes of nonlocal nonlinear boundary value problems including unknown definite integrals

• Project/Area Number: 18540224
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ryukoku University
• Principal Investigator: YOTSUTANI Shoji Ryukoku University, 理工学部, 教授 (60128361)
• Co-Investigator(Kenkyū-buntansha): MORITA Yoshihisa 龍谷大学, 理工学部, 教授 (10192783) ; MATSUMOTO Waichiro 龍谷大学, 理工学部, 教授 (40093314) ; OKA Hiroe 龍谷大学, 理工学部, 教授 (20215221) ; NINOMIYA Hirokazu 龍谷大学, 理工学部, 准教授 (90251610)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥630,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: 非線形現象 / 大域的分岐構造 / Cahn-Hilliard equation / 楕円関数 / 完全楕円積分 / 線形化固有値問題 / 非局所 / 非線形境界値問題 / ふりこの方程式 / Sturm-Liouville理論 / 反応拡散方程式 / Chan-Hilliard equation

Research Abstract

微分方程式の係数の中に解自身の定積分項を含む、非局所非線形境界値問題は、物性物理学や微分幾何学等にあらわれるが、大域的解構造の解明の手法は数年前に研究代表者により突破口が開かれ、今回の研究課題遂行結果、応用範囲が拡がり、手法も深化した。従来未解明であった、Cahn-Hilliard方程式の空間1次元定常解の大域的分岐構造を完全に解明した。さらに、反応拡散方程式の定常解のまわりでの線形化固有値問題の固有値を決定する超越方程式、および、固有関数を表示する方法を発見し、その超越方程式の解析手法を示した。

Research Products

• [Journal Article] An entire solution to the Lotka-Volterra competition-diffusion equations (2009)
  • Author(s): Y. Morita, K. Tachibana
  • Journal Title: SIAM J. Math. Anal. 40 Pages: 2217-2240
  • Peer Reviewed
• [Journal Article] Representation formulas for some 1-dimensional linearied eigenvalue problems (2008)
  • Author(s): T. Wakasa and S. Yotsutani
  • Journal Title: Communication on Pure and Applied Analysis 7 Pages: 665-682
  • Peer Reviewed
• [Journal Article] Monostable-type traveling waves of bistable reaction-diffusion equations in the multi-dimensional space (2008)
  • Author(s): Y. Morita and H. Ninomiya
  • Journal Title: Bull. Inst. Math. Acad. Sin. (N. S.) 3 Pages: 567-584
  • Peer Reviewed
• [Journal Article] Quantitative hyperbolicity estimates in one-dimensional dynamics (2008)
  • Author(s): S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka and P. Pilarczyk
  • Journal Title: Nonlinearity 21 Pages: 1967-1987
  • Peer Reviewed
• [Journal Article] Representation formulas for some l-dimensional Linearied eigenvalue problems (2008)
  • Author(s): T. Wakasa, S. Yotsutani
  • Journal Title: Communication on Pure and Applied Analysis 7 Pages: 665-682
  • Peer Reviewed
• [Journal Article] Monostable-type traveling waves of bistable reaction-diffusion equations in the multi-dimensional space- (2008)
  • Author(s): Y. Morita, H. Ninomiya
  • Journal Title: Bull. Inst. Math. Acad. Sin. (N. S. ) 3 Pages: 567-584
  • Peer Reviewed
• [Journal Article] Representation formulas for some 1-dimensional linearized eigenvalue problems (2008)
  • Author(s): T.Wakasa and S.Yotsutani
  • Journal Title: Cotntnunication on Pure and Applied Analysis 7(to appear) Pages: 665-682
  • Peer Reviewed
• [Journal Article] Stationary solutions to the one-dimensional Cahn-Hilliard equation (2007)
  • Author(s): S. Kosugi, Y. Morita and S. Yotsutani
  • Journal Title: Proof by the complete elliptic integrals, Discrete Conti. Dynam. Systems 19 Pages: 609-629
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex and boundary-vortex solutions in a Ginzburg-Landau model (2007)
  • Author(s): C.-N. Chen and Y. Morita
  • Journal Title: Nonlinearity 20 Pages: 943-964
  • Peer Reviewed
• [Journal Article] Topological horseshoes of travelling waves for a fast-slow predator-prey system (2007)
  • Author(s): M. Gameiro, T. Gedeon, W. Kalies, H. Kokubu, K. Mischaikow and H. Oka
  • Journal Title: Journal of Dynamics and Diff. Eq 19 Pages: 623-654
  • Peer Reviewed
• [Journal Article] Stationary solutions to the one-dimensional Cahn-Hilliard equation: Proof by the complete elliptic integrals (2007)
  • Author(s): S.Kosugi, Y.Morita and S.Yotsutan
  • Journal Title: Discrete Conti. Dynam. Systems 19 Pages: 609-629
  • Peer Reviewed
• [Journal Article] Bifurcation of vortex and boundaryvortex solutions in a Ginzburg-Landau model (2007)
  • Author(s): C.-N. Chen and Y.Morita
  • Journal Title: Nonlinearity 20 Pages: 943-964
  • Peer Reviewed
• [Journal Article] Stationary solutions to the one-dimensional Cahn-Hilliard equation : Proof by the complete elliptic integrals (2007)
  • Author(s): S.Kosugi, Y.Morita, S.Yotsutani
  • Journal Title: Discrete Conti. Dynam. Systems (to appear)
• [Journal Article] Representation formulas for some 1-dimensional linearized eigenvalue problems (2007)
  • Author(s): T.Wakasa, S.Yotsutani
  • Journal Title: Communication on Pure, Applied Analysis (to appear)
• [Journal Article] One can hear the shape of some non-convex drums (2007)
  • Author(s): W.Matsumoto, M.Murai, S.Yotsutani
  • Journal Title: Proc. 5th ISAAC Congress, Univ. Catania (to appear)
• [Journal Article] Phase pattern in a Ginzburg-Landaumodel with a discontinuous coefficient in a ring (2006)
  • Author(s): S. Kosugi and Y. Morita
  • Journal Title: Discrete Conti. Dynam. Systems 14 Pages: 140-148
  • Peer Reviewed
• [Journal Article] Entire solutions with merging fronts to reaction-diffusion equations (2006)
  • Author(s): Y. Morita and H. Ninomiya
  • Journal Title: J. Dynam. Differential Equations 18 Pages: 841-861
  • Peer Reviewed
• [Journal Article] Diffusion, cross-diffusion and competitive interaction (2006)
  • Author(s): M. Iida, M. Mimura and H. Ninomiya
  • Journal Title: J. Math. Biol 23 Pages: 617-641
  • Peer Reviewed
• [Journal Article] Phase pattern in a Ginzburg-Landau model with a discontinuous coefficient in a ring (2006)
  • Author(s): S.Kosugi, Y.Morita
  • Journal Title: Discrete Conti. Dynam. Systems 14 Pages: 140-148
• [Journal Article] Entire solutions withmerging fronts to reaction-diffusion equations (2006)
  • Author(s): Y.Morita, H.Ninomiya
  • Journal Title: J. Dynam. Differential Equations 18・4 Pages: 841-861
• [Journal Article] Diffusion, cross-diffusion and competitive interaction (2006)
  • Author(s): M.Iida, M.Mimura, H.Ninomiya
  • Journal Title: J. Math. Biol. 53・4 Pages: 617-641
• [Presentation] On some linearized eigenvalue problems associated with Chafee-Infante equation (2008)
  • Author(s): T. Wakasa and S. Yotsutani
  • Organizer: World Congress of Nonlinear Analysis
  • Place of Presentation: Orlando, Florida, US
  • Year and Date: 2008-07-07
• [Presentation] On some linearized eigenvalue problems associated with Chafee-Infante equation (2008)
  • Author(s): T. Wakasa, S. Yotsutani
  • Organizer: World Congress of Nonlinear Analysis 2008
  • Place of Presentation: Orlando, Florida, US
  • Year and Date: 2008-07-07
• [Presentation] Bifurcation analysis for a Ginzburg-Landau model (2008)
  • Author(s): Y. Morita
  • Organizer: Taida Institute of Mathematical Science
  • Place of Presentation: National Taiwan University
  • Year and Date: 2008-05-31
• [Presentation] Bifurcation analysis for a Ginzburg-Landau (2007)
  • Author(s): Y. Morita
  • Organizer: Equadiff 07
  • Place of Presentation: Vienna, Austria
• [Presentation] Bifurcation of vortex solutions in a Ginzburg-Landau model for small kappa (2007)
  • Author(s): Y. Morita
  • Organizer: International Conference on Mathematical Theory of Superconductivity and Liquid Crystals
  • Place of Presentation: East China Normal University
• [Presentation] Bifurcation analysis for a Ginzburg-Landau model (2007)
  • Author(s): Y.Morita
  • Organizer: Equadiff 07
  • Place of Presentation: Vienna University of Technology Vienna,Austria
• [Book] A Reactio-Diffusion Approximation to a Cross-Diffusion System, Recent Advances on Elliptic and Parabolic Issues (eds by M. Chipot and H. Ninomiya) (2006)
  • Author(s): M. Iida, and H. Ninomiya
  • Publisher: World Scientific Publishing
• [Book] Recent Advances on Elliptic and Parabolic Issues, eds by M.Chipot and H. Ninomiya (2006)
  • Author(s): M.Iida, H.Ninomiya
  • Publisher: A Reaction-Diffusion Approximation to a Cross-Diffusion System
• [Remarks]
  • URL: http://www.ryukoku.ac.jp/who/detail/592188/
• [Remarks]
  • URL: http://www.ryukoku.ac.jp/who/detail/592188/
• [Remarks]
  • URL: http://www.math.ryukoku.ac.jp/faculty.shtml
• [Remarks]
  • URL: http://www.ryukoku.ac.jp/who/who.php?uid=141