A study of dynamics of a traveling wave and a interface in nonlinear diffusion equations

非线性扩散方程中行波和界面的动力学研究

• 批准号: 19740092
• 负责人: YAGISITA Hiroki
• 金额: $ 1.57万
• 依托单位: Kyoto Sangyo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19740092/
• 关键词: 応用数学; 解析学; 関数方程式論; 応用解析学; 非線形現象; 非線形解析学; 拡散方程式; 放物型微分方程式; 力学系; 放物型偏微分方程式; 曲率流方程式; 界面ダイナミクス; 進行波解; 非線形偏微分方程式

The diffusion phenomenon of the nonlinear system appears in a lot of fields like physics, chemistry, biology, and recently, the financial engineering etc. In them, the localized structure that is called an interface where a rapid state variation concentrates on the narrow confine appears, and there are a lot that understanding the behavior that this interface shows becomes a key to clarify a nonlinear phenomenon. The traveling wave solution is a special solution that composes this interface. In the present study, the dynamics of the interface and the traveling wave in the nonlinear diffusion phenomenon was mathematically analyzed.

非线性系统的扩散现象出现在物理、化学、生物以及最近的金融工程等许多领域，其中出现了一种局部化结构，称为快速状态变化集中在狭窄范围内的界面，了解这种界面所表现出的行为成为解释非线性现象的关键。行波解是构成这种界面的一种特殊解。本文对非线性扩散现象中的界面和行波的动力学进行了数学分析。

项目成果

Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach

• DOI: 10.2977/prims/1260476649
• 发表时间: 2008-10
• 期刊: Publications of The Research Institute for Mathematical Sciences
• 影响因子: 1.2
• 作者: Hiroki Yagisita

The spreading speeds of disturbance in a nonlocal Fisher equation

非局部 Fisher 方程中扰动的传播速度

• 发表时间: 2009
• 期刊: 京都産業大学論集. 自然科学系列 Vol.38
• 作者: 柳下浩紀