# American Institute of Mathematical Sciences

September  2019, 18(5): 2457-2472. doi: 10.3934/cpaa.2019111

## Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian

 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

* Corresponding author

Received  May 2018 Revised  November 2018 Published  April 2019

In this paper, we study the asymptotic stability of traveling wave fronts to the Allen-Cahn equation with a fractional Laplacian. The main tools that we used are super- and subsolutions and squeezing methods.

Citation: Luyi Ma, Hong-Tao Niu, Zhi-Cheng Wang. Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2457-2472. doi: 10.3934/cpaa.2019111
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