Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Abstract

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: ${\delta }_{t}u=J\times u-u+f(x,u)t\in R^{+},x\in R^N$, 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.

Annales de l'Institut Henri Poincaré Analyse non linéaire (2011)

References in corpus (3)

• On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators
• Nonlocal anisotropic dispersal with monostable nonlinearity
• Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity