Asymptotic Behavior of a Nonlocal KPP Equation with an Almost Periodic Nonlinearity

2014/11/19 by Yan Zhang, Zhang, Yan
Mathematics · #35B27 #35B40 (Primary) #35D40 (Secondary) #35K57 #35R09 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B27 #msc:35B40 #msc:35D40 #msc:35K57 #msc:35R09

paper · pdf · doi:10.48550/arxiv.1411.5095

15 pages

arxiv created 2016/01/18 · arxiv updated 2016/01/19

Abstract

We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (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.

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