# American Institute of Mathematical Sciences

September  2016, 36(9): 5183-5199. doi: 10.3934/dcds.2016025

## Asymptotic behavior of a nonlocal KPP equation with an almost periodic nonlinearity

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Received  December 2014 Revised  February 2016 Published  May 2016

We consider a space-inhomogeneous KPP equation with a nonlocal diffusion and an almost-periodic nonlinearity. By employing and adapting the theory of homogenization, we show that solutions of this equation asymptotically converge to its stationary states in regions of space separated by a front that is determined by a Hamilton-Jacobi variational inequality.
Citation: Yan Zhang. Asymptotic behavior of a nonlocal KPP equation with an almost periodic nonlinearity. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5183-5199. doi: 10.3934/dcds.2016025
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