# American Institute of Mathematical Sciences

April  2015, 35(4): 1589-1607. doi: 10.3934/dcds.2015.35.1589

## Pattern formation in a cross-diffusion system

 1 Institute for Mathematical Sciences, Renmin University of China, Haidian District, Beijing, 100872, China 2 Center for Partial Differential Equations, East China Normal University, Minhang, Shanghai, 200241 3 Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, Shiga 520-2194

Received  August 2013 Revised  June 2014 Published  November 2014

In this paper we study the Shigesada-Kawasaki-Teramoto model [17] for two competing species with cross-diffusion. We prove the existence of spectrally stable non-constant positive steady states for high-dimensional domains when one of the cross-diffusion coefficients is sufficiently large while the other is equal to zero.
Citation: Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589
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