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

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.

26 pages

References in corpus (2)

• Nonlocal anisotropic dispersal with monostable nonlinearity
• Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion