Traveling wave solutions of a reaction-diffusion equation with state-dependent delay

Guo Lin, Haiyan Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

Original languageEnglish (US)
Pages (from-to)319-334
Number of pages16
JournalCommunications on Pure and Applied Analysis
Volume15
Issue number2
DOIs
StatePublished - Mar 1 2016

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State-dependent Delay
Traveling Wave Solutions
Reaction-diffusion Equations
Monotone
Upper and Lower Solutions
Wave Speed
Nonexistence
Fixed point theorem

Keywords

  • Asymptotic spreading
  • Comparison principle
  • Minimal wave speed

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. / Lin, Guo; Wang, Haiyan.

In: Communications on Pure and Applied Analysis, Vol. 15, No. 2, 01.03.2016, p. 319-334.

Research output: Contribution to journalArticle

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