Pattern formation in a cross-diffusion system

Yuan Lou; Wei-Ming Ni; Shoji Yotsutani

doi:10.3934/dcds.2015.35.1589

Article Contents

2015, Volume 35, Issue 4: 1589-1607. Doi: 10.3934/dcds.2015.35.1589

This issue Previous Article Spiraling bifurcation diagrams in superlinear indefinite problems Next Article Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats

Pattern formation in a cross-diffusion system

1.
Institute for Mathematical Sciences, Renmin University of China, Haidian District, Beijing, 100872
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: July 31, 2013

Revised: May 31, 2014

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 92D25, 92D40.

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