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

Fang Li; Kimie Nakashima; Wei-Ming Ni

doi:10.3934/dcds.2008.20.259

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2008, Volume 20, Issue 2: 259-274. Doi: 10.3934/dcds.2008.20.259

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

1.
School of Mathematics, University of Minnesota, Minneapolis, MN55455
2.
Department of Ocean Science, Tokyo University of Marine Sciences and Technology, 4-5-7, Konan, Minato-ku, Tokyo 108-8477
3.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received: December 31, 2006

Revised: July 31, 2007

Published: April 2008

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Abstract

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.

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Mathematics Subject Classification: 35K57, 35B35.

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