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Spatial Dynamics of A Reaction-Diffusion Model with DistributedDelay

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: [email protected]
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Abstract

This paper is devoted to the study of spreading speeds and traveling waves for a class ofreaction-diffusion equations with distributed delay. Such an equation describes growth anddiffusion in a population where the individuals enter a quiescent phase exponentially andstay 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 ofmonostable traveling waves are established via the finite-delay approximation approach. Wealso prove the existence of bistable traveling waves in the case where the associatedreaction system admits a bistable structure. Moreover, the global stability and uniquenessof the bistable waves are obtained in the case where the density function has zerotail

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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