Geodesic
Spatial Dynamics of A Reaction-Diffusion Model with Distributed Delay
Y. Zhang1 ; X.-Q. Zhao1
1 Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s, NL A1C 5S7, Canada
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 60-77.

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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
DOI : 10.1051/mmnp/20138306

Y. Zhang 1 ; X.-Q. Zhao 1

1 Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s, NL A1C 5S7, Canada 
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Y. Zhang; X.-Q. Zhao. Spatial Dynamics of A Reaction-Diffusion Model with Distributed Delay. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 60-77. doi : 10.1051/mmnp/20138306. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138306/

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