Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

Cheng Hsiung Hsu, Tzi Sheng Yang, Zhixian Yu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

Original languageEnglish
Pages (from-to)838-863
Number of pages26
JournalNonlinearity
Volume31
Issue number3
DOIs
StatePublished - 7 Feb 2018

Keywords

  • comparison principle
  • reaction diffusion system
  • stability
  • traveling waves
  • weighed energy method

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