Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains

study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 0, this behavior is given by a multiple of the dipole solution for...

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Autor principal: Wolanski, Noemi Irene
Publicado: 2016
Materias:
Asymptotic behavior
Exterior domain
Matched asymptotics
Nonlocal diffusion
Asymptotic analysis
Diffusion
Asymptotic behaviors
Dirichlet data
First moments
Large time behavior
Stationary solutions
Partial differential equations
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v48_n3_p1549_Cortazar
http://hdl.handle.net/20.500.12110/paper_00361410_v48_n3_p1549_Cortazar
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00361410_v48_n3_p1549_Cortazar
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spelling paper:paper_00361410_v48_n3_p1549_Cortazar2023-06-08T15:01:56Z Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains Wolanski, Noemi Irene Asymptotic behavior Exterior domain Matched asymptotics Nonlocal diffusion Asymptotic analysis Diffusion Asymptotic behaviors Dirichlet data Exterior domain First moments Large time behavior Matched asymptotics Nonlocal diffusion Stationary solutions Partial differential equations study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R.: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t1/2h(t), limt→h(t) = 0, the solution scaled by a factor t3/2/(|x| + 1) converges to a stationary solution of the problem that behaves as b±x as x ±. The constants b± are obtained through a matching procedure with the far field limit. In the very far field, |x|≤t1/2g(t), g(t)→, the solution decays as o(t-1). © by SIAM. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v48_n3_p1549_Cortazar http://hdl.handle.net/20.500.12110/paper_00361410_v48_n3_p1549_Cortazar
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 behavior
Exterior domain
Matched asymptotics
Nonlocal diffusion
Asymptotic analysis
Diffusion
Asymptotic behaviors
Dirichlet data
Exterior domain
First moments
Large time behavior
Matched asymptotics
Nonlocal diffusion
Stationary solutions
Partial differential equations
spellingShingle Asymptotic behavior
Exterior domain
Matched asymptotics
Nonlocal diffusion
Asymptotic analysis
Diffusion
Asymptotic behaviors
Dirichlet data
Exterior domain
First moments
Large time behavior
Matched asymptotics
Nonlocal diffusion
Stationary solutions
Partial differential equations
Wolanski, Noemi Irene
Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
topic_facet Asymptotic behavior
Exterior domain
Matched asymptotics
Nonlocal diffusion
Asymptotic analysis
Diffusion
Asymptotic behaviors
Dirichlet data
Exterior domain
First moments
Large time behavior
Matched asymptotics
Nonlocal diffusion
Stationary solutions
Partial differential equations
description study the large time behavior of solutions to the nonlocal diffusion equation ℓtu = J-u-u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ζ1 ≤ |x|t.1/2 ≤ ζ2, ζ1, ζ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R.: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t1/2h(t), limt→h(t) = 0, the solution scaled by a factor t3/2/(|x| + 1) converges to a stationary solution of the problem that behaves as b±x as x ±. The constants b± are obtained through a matching procedure with the far field limit. In the very far field, |x|≤t1/2g(t), g(t)→, the solution decays as o(t-1). © by SIAM.
author Wolanski, Noemi Irene
author_facet Wolanski, Noemi Irene
author_sort Wolanski, Noemi Irene
title Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_short Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_full Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_fullStr Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_full_unstemmed Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_sort asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v48_n3_p1549_Cortazar
http://hdl.handle.net/20.500.12110/paper_00361410_v48_n3_p1549_Cortazar
work_keys_str_mv AT wolanskinoemiirene asymptoticbehaviorforaonedimensionalnonlocaldiffusionequationinexteriordomains
_version_ 1768542073403736064

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