Time periodic traveling wave solutions for periodic advection-reaction-diffusion systems

Guangyu Zhao, Shigui Ruan

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection-reaction-diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c* such that for each wave speed c≤c*, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c≤c* are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves with speed c>c*.

Original languageEnglish (US)
Pages (from-to)1078-1147
Number of pages70
JournalJournal of Differential Equations
Volume257
Issue number4
DOIs
StatePublished - Aug 15 2014

Keywords

  • Advection-reaction-diffusion system
  • Asymptotic stability
  • Lotka-Volterra competition system
  • Maximal wave speed
  • Time periodic traveling waves

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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