Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GLOBAL EXISTENCE OF SOLUTIONS TO THE PREY-PREDATOR SYSTEM WITH A SINGLE CROSS-DIFFUSION

  • Shim, Seong-A (DEPARTMENT OF MATHEMATICS, SUNGSHIN WOMEN'S UNIVERSITY)
  • Published : 2006.05.01
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Abstract

The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\;{\leq}\;{\infty}$. By obtaining the bounds of $W\array_2^1$-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 $d_1\;and\;d_2$ are sufficiently large.

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References

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