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Spatial Dynamics of A Reaction-Diffusion Model with Distributed Delay

Published online by Cambridge University Press:  12 June 2013

Y. Zhang  and
X.-Q. Zhao
Y. Zhang
Affiliation:
Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s, NL A1C 5S7, Canada
X.-Q. Zhao*
Affiliation:
Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s, NL A1C 5S7, Canada
*
⋆ Corresponding author. E-mail: zhao@mun.ca
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Abstract

This paper is devoted to the study of spreading speeds and traveling waves for a class of reaction-diffusion equations with distributed delay. Such an equation describes growth and diffusion in a population where the individuals enter a quiescent phase exponentially and stay quiescent for some arbitrary time that is given by a probability density function. The existence of the spreading speed and its coincidence with the minimum wave speed of monostable traveling waves are established via the finite-delay approximation approach. We also prove the existence of bistable traveling waves in the case where the associated reaction system admits a bistable structure. Moreover, the global stability and uniqueness of the bistable waves are obtained in the case where the density function has zero tail

Keywords

Distributed delayspreading speedstraveling wavesglobal stability
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 3: Front Propagation , 2013 , pp. 60 - 77
Copyright
© EDP Sciences, 2013

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