On a nonlocal reaction-diffusion population model

Keng Deng

doi:10.3934/dcdsb.2008.9.65

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2008, Volume 9, Issue 1: 65-73. Doi: 10.3934/dcdsb.2008.9.65

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On a nonlocal reaction-diffusion population model

Keng Deng^1,

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010

Received: January 2007

Revised: August 2007

Published: January 2008

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Abstract

In this paper, we consider a nonlocal parabolic initial value problem that models a single species which is diffusing, aggregating, reproducing and competing for space and resources. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the problem. We also analyze the long-time behavior of the solution.

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Mathematics Subject Classification: 35A05, 35B40, 35K57, 92D25.

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