反应扩散系统双稳波前解的全局渐近稳定性

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 440-448.

反应扩散系统双稳波前解的全局渐近稳定性

吴事良, 刘三阳

西安电子科技大学应用数学系|西安 710071

收稿日期:2008-02-20 修回日期:2009-04-27 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
国家自然科学基金(60674108)和西安电子科技大学基本科研业务费(JY10000970005)资助.

Global Asymptotic Stability of Bistable Traveling Wave Front in Reaction-diffusion Systems

WU Shi-Liang, LIU San-Yang

Department of Applied Mathematics, Xidian University, Xi'an |710071

Received:2008-02-20 Revised:2009-04-27 Online:2010-04-25 Published:2010-04-25
Supported by:
国家自然科学基金(60674108)和西安电子科技大学基本科研业务费(JY10000970005)资助.

摘要/Abstract

摘要：

该文研究一类拟单调反应扩散系统的古典解的渐近行为. 在双稳的假定下, 利用上、下解方法和单调半流的收敛性结果,
证明了当系统的初值在±∞处的极限分别“大于''和”小于''其中间平衡点时, 初值问题的解收敛于一个连接两个稳定平衡点的波前解. 最后, 将结果应用到一个传染病模型.

关键词: 反应扩散系统, 双稳波前解, 全局渐近稳定性

Abstract:

This paper is concerned with the asymptotic behavior of classical solutions of a class of quasi-monotone
reaction-diffusion systems. Under bistable assumption, the authors show that if only the spatial limits of the initial value at ±∞ are larger and smaller than the immediate unstable equilibrium respectively, then the solutions of the corresponding initial value problem will converge to a bistable traveling front. The approach is based on the elementary super- and sub-solution comparison and the convergence results of monotone semiflows. As an application, these abstract results are applied to a system modeling man-environment-man epidemics.

Key words: Reaction-diffusion system, Bistable traveling wave front, Global asymptotic stability

中图分类号:

35K57

吴事良, 刘三阳. 反应扩散系统双稳波前解的全局渐近稳定性[J]. 数学物理学报, 2010, 30(2): 440-448.

WU Shi-Liang, LIU San-Yang. Global Asymptotic Stability of Bistable Traveling Wave Front in Reaction-diffusion Systems[J]. Acta mathematica scientia,Series A, 2010, 30(2): 440-448.

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