# American Institute of Mathematical Sciences

September  2017, 22(7): 3007-3022. doi: 10.3934/dcdsb.2017160

## Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations

 1 School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China 2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

* Corresponding author: Hongmei Cheng

Received  April 2016 Revised  April 2017 Published  May 2017

In this paper, we mainly discuss the existence and asymptotic stability of traveling fronts for the nonlocal evolution equations. With the monostable assumption, we obtain that there exists a constant $c^*>0$, such that the equation has no traveling fronts for $0<c<c^*$ and a traveling front for each cc*. For $c>c^*$, we will further show that the traveling front is globally asymptotic stable and is unique up to translation. If we applied to some differential equations or integro-differential equations, our results recover and/or complement a number of existing ones.

Citation: Hongmei Cheng, Rong Yuan. Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 3007-3022. doi: 10.3934/dcdsb.2017160
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