ScienceAsia 44 (2018): 422-431 |doi:
Exponential stability of travelling waves for a general
reaction-diffusion equation with spatio-temporal
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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||School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
||School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
* Corresponding author, E-mail: firstname.lastname@example.org
Received 10 Jun 2018, Accepted 12 Feb 2019