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http://dx.doi.org/10.4134/CKMS.2008.23.2.211

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

Shim, Seong-A (Department of Mathematics Sungshin Women's University)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.2, 2008 , pp. 211-227 More about this Journal
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 $W^{1_2}$-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 $W^{1_2}$-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;
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