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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.

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