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2003, Volume 9, Issue 5: 1193-1200. Doi: 10.3934/dcds.2003.9.1193
This issue Previous Article Periodic probability measures are dense in the set of invariant measures Next Article On the Newton method in robust control of fluid flow

Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion

  • 1.

    Department of Mathematics, University of Connecticut, Storrs, CT 06269

  • 2.

    Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609

  • 3.

    Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku 169-8555, Tokyo

Received:  July 2002
Revised:  December 2002
Published:  September 2003
Abstract / Introduction Related Papers Cited by
    Abstract
  • The Shigesada-Kawasaki-Teramoto model is a generalization of the classical Lotka-Volterra competition model for which the competing species undergo both diffusion, self-diffusion and cross-diffusion. Very few mathematical results are known for this model, especially in higher space dimensions. In this paper, we shall prove global existence of strong solutions in any space dimension for this model when the cross-diffusion coefficient in the first species is sufficiently small and when there is no self-diffusion or cross-diffusion in the second species.
    Mathematics Subject Classification: Primary: 35K55, 35K50, 92D40.

    Citation:
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