The stability of traveling waves for Allen-Cahn equations with fractional Laplacian

摘要

In this paper, we mainly consider the stability of traveling waves for the Allen-Cahn equation with fractional Laplacian. By the comparison principle and the perturbation theory, we can locate the spectrum of the linearized operator. Using the spectral analysis of the linearized operator, we obtain that the traveling waves are exponentially asymptotically stable.