# American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems - A, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681
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