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 Global existence of solutions to the Prey-Predator system with a single cross-diffusion Bull. Korean Math. Soc. 2006 Vol. 43, No. 2, 443-459 Published online June 1, 2006 Seong-A Shim Sungshin Women's University Abstract : The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\le \infty$. By obtaining the bounds of $W^1_2$-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 $d_1$ and $d_2$ are sufficiently large. Keywords : prey-predator system, single cross-diffusion, self-diffusion, calculus inequalities, $W^1_2$-bound, long-time behavior MSC numbers : 35K55, 35B40 Downloads: Full-text PDF