Pulsating fronts for nonlocal dispersion and KPP nonlinearity

TL;DR

This paper studies pulsating wave solutions in nonlocal reaction-diffusion equations with KPP nonlinearities, establishing their existence, minimal speed, and asymptotic behavior in heterogeneous media.

Contribution

It proves the existence of pulsating fronts, characterizes their minimal propagation speed, and provides bounds on their asymptotic behavior for nonlocal KPP equations.

Findings

Existence of pulsating fronts in nonlocal KPP equations.

Variational characterization of minimal wave speed.

Exponential bounds on solution asymptotics.

Abstract

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $\delta_tu = J \times u - u + f (x, u) t \in R^+, x \in R^N$, where J is a probability density and f is a KPP nonlinearity periodic in the x variables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the 0 state by a heterogeneous state. We also give a variational characterization of the minimal speed of such pulsating fronts and exponential bounds on the asymptotic behavior of the solution.