Spatial Dynamics of A Reaction-Diffusion Model with Distributed Delay

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 arbit...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2013-01, Vol.8 (3), p.60-77
Main Authors: Zhang, Y., Zhao, X.-Q.
Format: Article
Language:English
Subjects:
35Q92
39B72
92B05
92D25
Diffusion
Distributed delay
global stability
Mathematical models
Propagation
spreading speeds
traveling waves
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Summary: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
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/20138306