A nonlocal convection-diffusion equation

En:

J. Funct. Anal. 2007;251(2):399-437

Fecha:

2007

Formato:

application/pdf

Tipo de documento:

info:eu-repo/semantics/article
info:ar-repo/semantics/artículo
info:eu-repo/semantics/publishedVersion

Descriptores:

Asymptotic behaviour -  Convection-diffusion -  Nonlocal diffusion

Descripción:

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J * u - u + G * (f (u)) - f (u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equation ut = Δ u + b ṡ ∇ (f (u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection-diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t → ∞ when f (u) = | u |q - 1 u with q > 1. We find the decay rate and the first-order term in the asymptotic regime. © 2007 Elsevier Inc. All rights reserved.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Identificador(es):

http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat

Derechos:

info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar