Electron. J. Diff. Equ., Vol. 2016 (2016), No. 86, pp. 1-15.

Exponential stability of traveling waves for non-monotone delayed reaction-diffusion equations

Yixin Liu, Zhixian Yu, Jing Xia

Abstract:
This article concerns the exponential stability of non-critical traveling waves (the wave speed is greater than the minimum speed) for non-monotone time-delayed reaction-diffusion equations. With the help of the weighted energy method, we prove that the non-critical travelling waves are exponentially stable when the initial perturbation around the wave is small.

Submitted July 20, 2015. Published March 29, 2016.
Math Subject Classifications: 35C07, 92D25, 35B35.
Key Words: Stability; non-monotone; weighted energy method.

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Yixin Liu
College of Science
University of Shanghai for Science and Technology
Shanghai, 200093, China
email: 838080693@qq.com
Zhixian Yu
College of Science
University of Shanghai for Science and Technology
Shanghai, 200093, China
email: zxyu@usst.edu.cn, zxyu0902@163.com
Jing Xia
Department of Fundamental Courses
Academy of Armored Force Engineering
Beijing 100072, China
email: xiajingcjh@163.com

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