GLOBAL EXISTENCE OF SOLUTIONS TO THE PREY-PREDATOR SYSTEM WITH A SINGLE CROSS-DIFFUSION

Title & Authors
GLOBAL EXISTENCE OF SOLUTIONS TO THE PREY-PREDATOR SYSTEM WITH A SINGLE CROSS-DIFFUSION
Shim, Seong-A;

Abstract
The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $\small{T\;{\leq}\;{\infty}}$. By obtaining the bounds of $\small{W\array_2^1}$-norms of the local solution independent of T we establish the global existence of the solution. And the long-time behaviors of the global solution are analyzed when the diffusion rates $\small{d_1\;and\;d_2}$ are sufficiently large.
Keywords
prey-predator system;single cross-diffusion;self-diffusion;calculus inequalities;$\small{W\array_2^1}$-bound;long-time behavior;
Language
English
Cited by
1.
CONVERGENCE PROPERTIES OF PREDATOR-PREY SYSTEMS WITH FUNCTIONAL RESPONSE,;

호남수학학술지, 2008. vol.30. 3, pp.411-423
1.
CONVERGENCE PROPERTIES OF PREDATOR-PREY SYSTEMS WITH FUNCTIONAL RESPONSE, Honam Mathematical Journal, 2008, 30, 3, 411
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