Analysis of interface motion and blow-up phenomena in nonlinear partial differential equations

非线性偏微分方程中的界面运动和爆炸现象分析

• 批准号: 20340033
• 负责人: MATANO Hiroshi
• 金额: $ 11.98万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20340033/
• 关键词: 非線形問題; 非線形偏微分方程式; 進行波; 特異性; 界面運動; 解の爆発; 電気生理学; 非線形現象; 安定性; 特異極限; 組みひも群; 爆発現象; 均質化極限

This research project deals with such themes as (1) traveling waves in nonlinear diffusion equations, (2) singular limit of nonlinear diffusion equations and interface motion, (3) blow-up in nonlinear heat equations, (4) mathematical analysis of 3D cellular electrophysiological model. The theme (4) was added after the program began. In theme (1), we studied, among other things, traveling waves colliding with obstacles, the stability of planar waves, and the problem of maximizing traveling wave speeds. In theme (3) we studied, among other things, classification of blow-up in Sobolev superlinear heat equations, and an application the theory of braid groups to the dead-core problem.

本课题主要研究方向为：(1)非线性扩散方程中的行波，(2)非线性扩散方程和界面运动的奇异极限，(3)非线性热方程的爆破，(4)三维细胞电生理模型的数学分析。主题(4)是在节目开始后添加的。在主题(1)中，我们研究了行波与障碍物的碰撞、平面波的稳定性以及行波速度最大化问题。在主题(3)中，我们研究了Sobolev超线性热方程的爆破分类，以及辫群理论在死核问题中的应用。

项目成果

A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations

• DOI: 10.1090/s0002-9947-2010-04931-1
• 发表时间: 2010-04
• 期刊: Transactions of the American Mathematical Society
• 影响因子: 1.3
• 作者: Xing Liang;Xiaotao Lin;H. Matano

Front propagation in spatially stratified environments

空间分层环境中的前向传播

• 发表时间: 2008
• 作者: Toshio Sakata;Lin Chen;Toshio Sumi;Mitsuhiro Miyazaki;長井 英生;俣野博
• 通讯作者: 俣野博

Classification of type I and type II behaviors for a supercritical nonlinear heat equation

• DOI: 10.1016/j.jfa.2008.05.021
• 发表时间: 2009-02
• 期刊: Journal of Functional Analysis
• 影响因子: 1.7
• 作者: H. Matano;F. Merle

Front propagation in hyperbolic space

双曲空间中的前传播

• 发表时间: 2010
• 作者: K.Kuramoto;et al;舟木直久;Kensuke Homma;荻尾彰一;K. Homma;舟木直久;S.Ogio on behalf of TA collaboration;Kensuke Homma;舟木直久;俣野博
• 通讯作者: 俣野博

An application of braid group theory to the finite time dead-core rate

• DOI: 10.1007/s00028-010-0072-0
• 发表时间: 2010-05
• 期刊: Journal of Evolution Equations
• 影响因子: 1.4
• 作者: Jong-Shenq Guo;H. Matano;Chin-Chin Wu-Chin