# American Institute of Mathematical Sciences

December  2008, 22(4): 1091-1120. doi: 10.3934/dcds.2008.22.1091

## Exponential attractors for competing species model with cross-diffusions

 1 Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871

Received  June 2007 Revised  November 2007 Published  September 2008

This paper is concerned with the competing species model presented by Shigesada-Kawasaki-Teramoto in 1979. Under a suitable condition on self-diffusions and cross-diffusions, we construct a dynamical system determined from the model. Furthermore, under the same condition we construct exponential attractors of the dynamical system.
Citation: Atsushi Yagi. Exponential attractors for competing species model with cross-diffusions. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 1091-1120. doi: 10.3934/dcds.2008.22.1091
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