# American Institute of Mathematical Sciences

February  2017, 37(2): 1013-1037. doi: 10.3934/dcds.2017042

## Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity

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

* Corresponding author

Received  December 2014 Revised  July 2015 Published  November 2016

The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with finite speed and space regularity in the sense of uniform Lipschitz continuity. Our approach is first constructing a sequence of approximating front-like solutions and then proving that the approximating solutions converge to a transition front. We take advantage of the idea of modified interface location, which allows us to characterize the finite speed of approximating solutions in the absence of space regularity, and leads directly to uniform exponential decaying estimates.

Citation: Wenxian Shen, Zhongwei Shen. Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 1013-1037. doi: 10.3934/dcds.2017042
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##### References:
Modified Interface Location
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