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

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September 2003, 9(5): 1193-1200. doi: 10.3934/dcds.2003.9.1193

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

Y. S. Choi ^1, , Roger Lui ^2, and Yoshio Yamada ^3,

1.	Department of Mathematics, University of Connecticut, Storrs, CT 06269, United States
2.	Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, United States
3.	Department of Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku 169-8555, Tokyo

Received July 2002 Revised December 2002 Published June 2003

Abstract
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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.

Keywords: self-diﬀusion, global existence., Cross-diﬀusion, a priori estimates.

Mathematics Subject Classification: Primary: 35K55, 35K50, 92D4.

Citation: Y. S. Choi, Roger Lui, Yoshio Yamada. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1193-1200. doi: 10.3934/dcds.2003.9.1193

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