A nonlocal inhomogeneous dispersal process
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Date
2007
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
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.
Description
Keywords
integral equation, nonlocal dispersal, inhomogeneous dispersal, TRAVELING-WAVES, DIFFUSION, EQUATIONS