Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1273-1281.

• Articles • Previous Articles     Next Articles

Existence of Travelling Wave Solutions for a Reaction-diffusion Equation with Nonlocal Delay

 LIANG Fei1,2, GAO Hong-Jun1   

  1. 1.Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210046;
    2.Department of Mathematics, An Hui Science &|Technology University, Anhui Fengyang |233100
  • Received:2009-10-20 Revised:2011-08-20 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    国家自然科学基金(10871097)和安徽省高等学校省级优秀人才基金(2011SQRL115)资助

Abstract:

This paper is concerned with the existence of a reaction-diffusion equation with nonlocal delay. For special kernels, by linear chain trick and geometric singular perturbation theory, the authors consider a natural connection between the existence of travelling wave solutions for the reaction-diffusion equation with nonlocal delay and the existence of travelling wave solutions for the corresponding undelayed reaction-diffusion equation. It is showed that if the corresponding undelayed reaction-diffusion equation has a travelling wave solution, then the reaction-diffusion with nonlocal delay also has a travelling wave solution for any sufficiently small delay.

Key words: Travelling wave solution, Nonlocal delay, Geometric singular perturbation

CLC Number: 

  • 35K57
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