Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 440-448.

• Articles • Previous Articles     Next Articles

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

WU Shi-Liang, LIU San-Yang   

  1. 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.

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

CLC Number: 

  • 35K57
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