Asymptotic Behavior of a Nonlocal KPP Equation with a Stationary Ergodic Nonlinearity

2014/11/20 by Yan Zhang, Zhang, Yan
Engineering · Mathematics · Medicine · #35B27 #35B40 (Primary) #35D40 (Secondary) #35K57 #35R09 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.AP #msc:35B27 #msc:35B40 #msc:35D40 #msc:35K57 #msc:35R09

paper · pdf · doi:10.48550/arxiv.1411.5423

26 pages

openalex publication_date 2014/11/20 · arxiv created 2014/12/07 · arxiv updated 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP) equation with a nonlocal diffusion and a stationary ergodic nonlinearity. By employing and adapting the theory of stochastic 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.

Citations

• Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion

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