Traveling wave solutions for time periodic reaction-diffusion systems

Wei Jian Bo, Guo Lin, Shigui Ruan

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

This paper deals with traveling wave solutions for time periodic reaction-diffiusion systems. The existence of traveling wave solutions is established by combining the fixed point theorem with super-and sub-solutions, which reduces the existence of traveling wave solutions to the existence of super-and sub-solutions. The asymptotic behavior is determined by the stability of periodic solutions of the corresponding initial value problems. To illustrate the abstract results, we investigate a time periodic Lotka-Volterra system with two species by presenting the existence and nonexistence of traveling wave solutions, which connect the trivial steady state to the unique positive periodic solution of the corresponding kinetic system.

Original languageEnglish (US)
Pages (from-to)4329-4351
Number of pages23
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume38
Issue number9
DOIs
StatePublished - Sep 2018

Keywords

  • Asymptotic behavior
  • Lotka-Volterra competitive system
  • Super- and sub-solutions

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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