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May  2008, 20(2): 259-274. doi: 10.3934/dcds.2008.20.259

Stability from the point of view of diffusion, relaxation and spatial inhomogeneity

Fang Li 1, , Kimie Nakashima 2, and  Wei-Ming Ni 3,

1. 

School of Mathematics, University of Minnesota, Minneapolis, MN55455, United States
2. 

Department of Ocean Science, Tokyo University of Marine Sciences and Technology, 4-5-7, Konan, Minato-ku, Tokyo 108-8477, Japan
3. 

School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received  January 2007 Revised  August 2007 Published  November 2007

In this paper, we study how stability properties of solutions to general reaction-diffusion systems are related to the diffusion coefficients, response rate, and spatial inhomogeneity. In particular, all eigenvalues of steady states to general shadow systems are completely determined, and some consequences are discussed.
Keywords: Reaction-diffusion equations, response rate, instability, spatial inhomogeneity., shadow systems.
Mathematics Subject Classification: 35K57, 35B3.
Citation: Fang Li, Kimie Nakashima, Wei-Ming Ni. Stability from the point of view of diffusion, relaxation and spatial inhomogeneity. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 259-274. doi: 10.3934/dcds.2008.20.259
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