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Research articles

ScienceAsia 44(2018): 422-431 |doi: 10.2306/scienceasia1513-1874.2018.44.422


Exponential stability of travelling waves for a general reaction-diffusion equation with spatio-temporal delays


Rui Yana, Guirong Liub,?

 
ABSTRACT:     This paper is concerned with the exponential stability of travelling waves for a general reaction-diffusion equation with spatio-temporal delays. Here the travelling waves may be monotone or non-monotone. More precisely, by means of the weighted-energy method and the nonlinear Halanay inequality, we can prove that the travelling waves of this equation are exponentially stable, when the initial perturbation around the wave is small in a weighted norm. In the end, we apply our results to some models.

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a School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
b School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

* Corresponding author, E-mail: lgr5791@sxu.edu.cn

Received 10 Jun 2018, Accepted 12 Feb 2019