Global exponential stability of traveling waves in monotone bistable systems

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14 Citations (Scopus)

Abstract

We study the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with some diffusion coefficients being zero. The main tools to obtain our results are comparison principle, suitably constructed super-sub solutions, and squeezing methods. No spectrum analysis of the linear operator associated with traveling front solutions under study is needed. Therefore, our results not only recover and/or complement earlier stability results in the literature, but also provide a simple method to show the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with positive diffusion coefficients.

Original languageEnglish
Pages (from-to)601-623
Number of pages23
JournalDiscrete and Continuous Dynamical Systems
Volume21
Issue number2
DOIs
Publication statusPublished - 2008 Jun

Keywords

  • Asymptotic stability
  • Bistable
  • Exponential stability
  • Monotone system
  • Reaction-diffusion system
  • Traveling front solution

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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