Traveling wave solutions for reaction-diffusion systems

Zhigui Lin, Michael Pedersen, Canrong Tian

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model.
Original languageEnglish
JournalNonlinear Analysis: Theory, Methods & Applications
Volume73
Issue number10
Pages (from-to)3303-3313
ISSN0362-546X
DOIs
Publication statusPublished - 2010

Keywords

  • Traveling wave
  • Mixed quasimonotonicity
  • Upper and lower solutions

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