# American Institute of Mathematical Sciences

June  2008, 21(2): 601-623. doi: 10.3934/dcds.2008.21.601

## Global exponential stability of traveling waves in monotone bistable systems

 1 Department of Mathematics, National Chung Cheng University, 168, University Road, Min-Hsiung, Chia-Yi 621, Taiwan

Received  January 2007 Revised  July 2007 Published  March 2008

We study the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with some diffusion coefficients being zero. The main tools to obtain our results are comparison principle, suitably constructed super-sub solutions, and squeezing methods. No spectrum analysis of the linear operator associated with traveling front solutions under study is needed. Therefore, our results not only recover and/or complement earlier stability results in the literature, but also provide a simple method to show the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with positive diffusion coefficients.
Citation: Je-Chiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 601-623. doi: 10.3934/dcds.2008.21.601
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