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Spatial Dynamics of A Reaction-Diffusion Model with DistributedDelay

Published online by Cambridge University Press:  12 June 2013

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

Type
Research Article
Copyright
© EDP Sciences, 2013

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