# American Institute of Mathematical Sciences

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July  2016, 15(4): 1193-1213. doi: 10.3934/cpaa.2016.15.1193

## Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media

 1 Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849 2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

Received  June 2015 Revised  January 2016 Published  April 2016

The present paper is devoted to the study of transition fronts of nonlocal Fisher-KPP equations in time heterogeneous media. We first construct transition fronts with exact decaying rates as the space variable tends to infinity and with prescribed interface location functions, which are natural generalizations of front location functions in homogeneous media. Then, by the general results on space regularity of transition fronts of nonlocal evolution equations proven in the authors' earlier work ([25]), these transition fronts are continuously differentiable in space. We show that their space partial derivatives have exact decaying rates as the space variable tends to infinity. Finally, we study the asymptotic stability of transition fronts. It is shown that transition fronts attract those solutions whose initial data decays as fast as transition fronts near infinity and essentially above zero near negative infinity.
Citation: Wenxian Shen, Zhongwei Shen. Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous media. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1193-1213. doi: 10.3934/cpaa.2016.15.1193
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