Math. Model. Nat. Phenom.
Volume 8, Number 3, 2013Front Propagation
|Page(s)||60 - 77|
|Published online||12 June 2013|
Spatial Dynamics of A Reaction-Diffusion Model with Distributed Delay
Department of Mathematics and Statistics Memorial
University of Newfoundland St. John’s, NL
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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
Mathematics Subject Classification: 35Q92 / 39B72 / 92B05 / 92D25
Key words: Distributed delay / spreading speeds / traveling waves / global stability
© EDP Sciences, 2013
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