Abstract

This article in devoted to the study of the nonlocal dispersal equationut (x, t) = under(∫, R) J (frac(x - y, g (y))) frac(u (y, t), g (y)) d y - u (x, t) in  R × [0, ∞), 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 → ∞, showing that they converge locally to zero. © 2007 Elsevier Inc. All rights reserved.