A nonlocal convection-diffusion equation

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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 cond...

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Autores principales: Ignat, L.I., Rossi, J.D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2007
Materias:
Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_00221236_v251_n2_p399_Ignat
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spelling paperaa:paper_00221236_v251_n2_p399_Ignat2023-06-12T16:43:50Z A nonlocal convection-diffusion equation J. Funct. Anal. 2007;251(2):399-437 Ignat, L.I. Rossi, J.D. Asymptotic behaviour Convection-diffusion Nonlocal diffusion 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. 2007 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
spellingShingle Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
Ignat, L.I.
Rossi, J.D.
A nonlocal convection-diffusion equation
topic_facet Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
description 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.
format Artículo
Artículo
publishedVersion
author Ignat, L.I.
Rossi, J.D.
author_facet Ignat, L.I.
Rossi, J.D.
author_sort Ignat, L.I.
title A nonlocal convection-diffusion equation
title_short A nonlocal convection-diffusion equation
title_full A nonlocal convection-diffusion equation
title_fullStr A nonlocal convection-diffusion equation
title_full_unstemmed A nonlocal convection-diffusion equation
title_sort nonlocal convection-diffusion equation
publishDate 2007
url http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat
work_keys_str_mv AT ignatli anonlocalconvectiondiffusionequation
AT rossijd anonlocalconvectiondiffusionequation
AT ignatli nonlocalconvectiondiffusionequation
AT rossijd nonlocalconvectiondiffusionequation
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