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January  2008, 9(1): 65-73. doi: 10.3934/dcdsb.2008.9.65

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  October 2007

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.
Keywords: monotone sequences, permanence., Nonlocal population model, existence-uniqueness, comparison principle.
Mathematics Subject Classification: 35A05, 35B40, 35K57, 92D2.
Citation: Keng Deng. On a nonlocal reaction-diffusion population model. Discrete and Continuous Dynamical Systems - B, 2008, 9 (1) : 65-73. doi: 10.3934/dcdsb.2008.9.65
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