反应扩散系统双稳波前解的全局渐近稳定性  

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

作　　者：吴事良[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学应用数学系,西安710071

出　　处：《数学物理学报（A辑）》2010年第2期440-448,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(60674108);西安电子科技大学基本科研业务费(JY10000970005)资助

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.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 results are applied to a system modeling man-environment-man epidemics.

关 键 词：反应扩散系统 双稳波前解 全局渐近稳定性 

分 类 号：O175.14[理学—数学]