A nonlocal inhomogeneous dispersal process

Abstract

This article in devoted to the study of the nonlocal dispersal equation

u(t)(x, t) = R integral J(x - y/g(y))u(y, t)/g(y) dy-u(x, t) in R x [0, infinity),

and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t -> infinity, showing that they converge locally to zero. (C) 2007 Elsevier Inc. All rights reserved.