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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

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 and Continuous Dynamical Systems, 2003, 9 (5) : 1193-1200. doi: 10.3934/dcds.2003.9.1193
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