Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems

Wan Tong Li, Guo Lin, Shigui Ruan

Research output: Contribution to journalArticle

158 Citations (Scopus)

Abstract

This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction-diffusion systems without monotonicity, which concludes two-species diffusion-competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non- quasimonotonicity condition. By using Schauder's fixed point theorem, a new cross-iteration scheme is given to establish the existence of travelling wave solutions. More precisely, by using such a new cross-iteration, we reduce the existence of travelling wave solutions to the existence of an admissible pair of upper and lower solutions which are easy to construct in practice. To illustrate our main results, we study the existence of travelling wave solutions in two delayed two-species diffusion-competition systems.

Original languageEnglish (US)
Pages (from-to)1253-1273
Number of pages21
JournalNonlinearity
Volume19
Issue number6
DOIs
StatePublished - Jun 1 2006

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Competition System
Traveling Wave Solutions
Reaction-diffusion System
traveling waves
species diffusion
Quasimonotonicity
iteration
Upper and Lower Solutions
Competition Model
Schauder Fixed Point Theorem
Iteration Scheme
problem solving
Diffusion Model
Monotonicity
theorems
Iteration
Term

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems. / Li, Wan Tong; Lin, Guo; Ruan, Shigui.

In: Nonlinearity, Vol. 19, No. 6, 01.06.2006, p. 1253-1273.

Research output: Contribution to journalArticle

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