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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.


Documento: Artículo
Título:A nonlocal convection-diffusion equation
Autor:Ignat, L.I.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Institute of Mathematics, the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
Departamento Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Palabras clave:Asymptotic behaviour; Convection-diffusion; Nonlocal diffusion
Página de inicio:399
Página de fin:437
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.


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---------- APA ----------
Ignat, L.I. & Rossi, J.D. (2007) . A nonlocal convection-diffusion equation. Journal of Functional Analysis, 251(2), 399-437.
---------- CHICAGO ----------
Ignat, L.I., Rossi, J.D. "A nonlocal convection-diffusion equation" . Journal of Functional Analysis 251, no. 2 (2007) : 399-437.
---------- MLA ----------
Ignat, L.I., Rossi, J.D. "A nonlocal convection-diffusion equation" . Journal of Functional Analysis, vol. 251, no. 2, 2007, pp. 399-437.
---------- VANCOUVER ----------
Ignat, L.I., Rossi, J.D. A nonlocal convection-diffusion equation. J. Funct. Anal. 2007;251(2):399-437.