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

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.

arXiv comment15 pages

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• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Nonlocal anisotropic dispersal with monostable nonlinearity
• Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion

Cited by in corpus (1)

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