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

Yan  Zhang

doi:10.3934/dcds.2016025

Article Contents

2016, Volume 36, Issue 9: 5183-5199. Doi: 10.3934/dcds.2016025

This issue Previous Article The $C$-regularized semigroup method for partial differential equations with delays Next Article Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing

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

Yan Zhang^1,

1.
35 River Drive S. Apt. 210, Jersey City, NJ 07310

Received: November 30, 2014

Revised: January 31, 2016

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R09, 35K57; Secondary: 35B27, 35B40.

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