北京科技大学学报2011，Vol.33Issue(2)：250-256,7.
基于Conley指标理论求解反应扩散方程的冲击波解
Solving the shock wave solutions of reaction-diffusion equations based on Conley index theory
摘要
Abstract
Based on Conley index theory, the shock wave solutions of a class of nonlinear reaction-diffusion equations were studied. Considering the diffusion coefficient as a system parameter, the existence of heteroclinic orbits of ordinary differential equations satisfied by traveling wave solutions is analyzed by using Conley index and Morse decompositions. The existence of saddle-focus and saddle-crunode style shock wave solutions of the reaction-diffusion equations is proved on the basis of an idea that the solitary waves and shock waves of partial differential equations correspond to the homoclinic orbits and heteroclinic orbits of ordinary differential equations.In particular, the existence and uniqueness of saddle-saddle style shock wave solutions are proved by using connection matrixes and transition matrixes, which are computed with Conley packages and Maple software by programming.关键词
微分方程/反应扩散方程/冲击波/Conley指标Key words
differential equations/ reaction-diffusion equations/ shock waves/ Conley index分类
数学引用本文复制引用
张柳,张晓丹..基于Conley指标理论求解反应扩散方程的冲击波解[J].北京科技大学学报,2011,33(2):250-256,7.基金项目
北京科技大学冶金工程研究院基础理论研究基金资助项目(No.00009503) （No.00009503）
