May  2006, 15(2): 681-701. doi: 10.3934/dcds.2006.15.681

Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations

1. 

Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, United States

2. 

Department of Mathematics, Hunan Normal University, Changsha, Hunan

Received  January 2005 Revised  October 2005 Published  March 2006

We investigate the local stability of traveling-wave solutions of the nonlinear reaction-diffusion equations in various weighted Banach spaces. New methods are used in analyzing the location of the spectrum. The result covers the stability results of the traveling-wave solutions of reaction-diffusion equations including the well known Fisher-KPP-type nonlinearity.
Citation: Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681
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