Math. Model. Nat. Phenom.
Volume 8, Number 3, 2013Front Propagation
|60 - 77
|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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.