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July  2004, 10(3): 719-730. doi: 10.3934/dcds.2004.10.719

Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled 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, Japan

Received  October 2002 Revised  June 2003 Published  January 2004

This paper is a continuation of [3] by the same authors to study the problem of global existence of strong solutions for the Shigesada-Kawasaki-Teramoto model. We shall prove global existence of strong solutions assuming that there are self- and cross-diffusions in the first species and there is no cross-diffusion in the second species. If self-diffusion is also present in the second species, then our result requires that the space dimension be less than 6.
Keywords: cross-diffusion, apriori estimates, self-diffusion, strongly-coupled, global existence..
Mathematics Subject Classification: 35K50, 35K55, 35K57, 92D4.
Citation: Y. S. Choi, Roger Lui, Yoshio Yamada. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 719-730. doi: 10.3934/dcds.2004.10.719
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