Pattern dynamics of reaction-diffusion systems and free boundary problems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26287024
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Meiji 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
• 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

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.

Free Research Field

非線形偏微分方程式論