# American Institute of Mathematical Sciences

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

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