A nonlocal convection-diffusion equation

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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Autor principal: Rossi, Julio Daniel
Publicado: 2007
Materias:
Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v251_n2_p399_Ignat
http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00221236_v251_n2_p399_Ignat
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spelling paper:paper_00221236_v251_n2_p399_Ignat2023-06-08T14:46:24Z A nonlocal convection-diffusion equation Rossi, Julio Daniel 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v251_n2_p399_Ignat 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)
topic Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
spellingShingle Asymptotic behaviour
Convection-diffusion
Nonlocal diffusion
Rossi, Julio Daniel
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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v251_n2_p399_Ignat
http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat
work_keys_str_mv AT rossijuliodaniel anonlocalconvectiondiffusionequation
AT rossijuliodaniel nonlocalconvectiondiffusionequation
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