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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Autores principales:	Cortázar, C., Elgueta, M., Quirós, F., Wolanski, N.
Formato:	JOUR
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00039527_v205_n2_p673_Cortazar
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00039527_v205_n2_p673_Cortazar2023-10-03T13:56:44Z Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes Cortázar, C. Elgueta, M. Quirós, F. Wolanski, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format	JOUR
author	Cortázar, C. Elgueta, M. Quirós, F. Wolanski, N.
spellingShingle	Cortázar, C. Elgueta, M. Quirós, F. Wolanski, N. Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
author_facet	Cortázar, C. Elgueta, M. Quirós, F. Wolanski, N.
author_sort	Cortázar, C.
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
url	http://hdl.handle.net/20.500.12110/paper_00039527_v205_n2_p673_Cortazar
work_keys_str_mv	AT cortazarc asymptoticbehaviorforanonlocaldiffusionequationindomainswithholes AT elguetam asymptoticbehaviorforanonlocaldiffusionequationindomainswithholes AT quirosf asymptoticbehaviorforanonlocaldiffusionequationindomainswithholes AT wolanskin asymptoticbehaviorforanonlocaldiffusionequationindomainswithholes
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Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

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