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Existence of Waves for a Nonlocal Reaction-DiffusionEquation

Published online by Cambridge University Press:  27 July 2010

I. Demin  and
V. Volpert
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Abstract

In this work we study a nonlocal reaction-diffusion equation arising in populationdynamics. The integral term in the nonlinearity describes nonlocal stimulation ofreproduction. We prove existence of travelling wave solutions by the Leray-Schauder methodusing topological degree for Fredholm and proper operators and special a priori estimatesof solutions in weighted Hölder spaces.

Keywords

integro-differential equationtravelling wavesLeray-Schauder method
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 80 - 101
Copyright
© EDP Sciences, 2010

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