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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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00221236_v251_n2_p399_Ignat_oai |
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I28-R145-paper_00221236_v251_n2_p399_Ignat_oai2020-10-19 Ignat, L.I. Rossi, J.D. 2007 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00221236_v251_n2_p399_Ignat info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Funct. Anal. 2007;251(2):399-437 Asymptotic behaviour Convection-diffusion Nonlocal diffusion A nonlocal convection-diffusion equation info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00221236_v251_n2_p399_Ignat_oai |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-145 |
collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
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 http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00221236_v251_n2_p399_Ignat_oai |
work_keys_str_mv |
AT ignatli anonlocalconvectiondiffusionequation AT rossijd anonlocalconvectiondiffusionequation AT ignatli nonlocalconvectiondiffusionequation AT rossijd nonlocalconvectiondiffusionequation |
_version_ |
1766026584343445504 |