[ W12 ]-ESTIMATES ON THE PREY-PREDATOR SYSTEMS WITH CROSS-DIFFUSIONS AND FUNCTIONAL RESPONSES

Title & Authors
[ W12 ]-ESTIMATES ON THE PREY-PREDATOR SYSTEMS WITH CROSS-DIFFUSIONS AND FUNCTIONAL RESPONSES
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 $\small{W^1_2}$-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 $\small{W^1_2}$-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
1.
On stability of two degenerate reaction–diffusion systems, Journal of Mathematical Analysis and Applications, 2012, 390, 1, 126
2.
EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY–PREDATOR MODEL WITH CROSS-DIFFUSION, International Journal of Biomathematics, 2010, 03, 02, 161
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