[ W^{1}_{2} ]-ESTIMATES ON THE PREY-PREDATOR SYSTEMS WITH CROSS-DIFFUSIONS AND FUNCTIONAL RESPONSES

- Journal title : Communications of the Korean Mathematical Society
- Volume 23, Issue 2, 2008, pp.211-227
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2008.23.2.211

Title & Authors

[ W^{1}_{2} ]-ESTIMATES ON THE PREY-PREDATOR SYSTEMS WITH CROSS-DIFFUSIONS AND FUNCTIONAL RESPONSES

Shim, Seong-A;

Shim, Seong-A;

Abstract

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain -estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform -bound of the solutions and obtain the global existence in time.

Keywords

quasilinear parabolic systems;calculus inequalities;local existence;global existence;cross-diffusions;self-diffusions;Holling-type II functional responses;uniform bounds;

Language

English

Cited by

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