Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J*u-u:= Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on ℝ N\\Ω. When the space dimension is three or more this behavior is given by a multiple of the...

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Autor principal: Wolanski, Noemi Irene
Publicado: 2012
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00039527_v205_n2_p673_Cortazar
http://hdl.handle.net/20.500.12110/paper_00039527_v205_n2_p673_Cortazar
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00039527_v205_n2_p673_Cortazar2023-06-08T14:24:49Z Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes Wolanski, Noemi Irene The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J*u-u:= Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on ℝ N\\Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation. © 2012 Springer-Verlag. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00039527_v205_n2_p673_Cortazar http://hdl.handle.net/20.500.12110/paper_00039527_v205_n2_p673_Cortazar
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J*u-u:= Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on ℝ N\\Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation. © 2012 Springer-Verlag.
author Wolanski, Noemi Irene
spellingShingle Wolanski, Noemi Irene
Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
author_facet Wolanski, Noemi Irene
author_sort Wolanski, Noemi Irene
title Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_short Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_full Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_fullStr Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_full_unstemmed Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_sort asymptotic behavior for a nonlocal diffusion equation in domains with holes
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00039527_v205_n2_p673_Cortazar
http://hdl.handle.net/20.500.12110/paper_00039527_v205_n2_p673_Cortazar
work_keys_str_mv AT wolanskinoemiirene asymptoticbehaviorforanonlocaldiffusionequationindomainswithholes
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