Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence

In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation (Formula presented.), with v(x, t) = g(x, t), (Formula presented.) can be approximated uniformly by solutions of nonlocal problems of the form (Formula presented.), with (Formula presented.) , (Formula p...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2016
Materias:
Evolution problems
Nonlocal diffusion
Spacial dependence
Mathematical techniques
Dirichlet problem
Evolution problem
Nonlocal problems
Parabolic Equations
Spatial dependence
Symmetric kernel
Partial differential equations
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00442275_v67_n3_p_Molino
http://hdl.handle.net/20.500.12110/paper_00442275_v67_n3_p_Molino
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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_00442275_v67_n3_p_Molino2023-06-08T15:05:00Z Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence Rossi, Julio Daniel Evolution problems Nonlocal diffusion Spacial dependence Mathematical techniques Dirichlet problem Evolution problem Nonlocal diffusion Nonlocal problems Parabolic Equations Spacial dependence Spatial dependence Symmetric kernel Partial differential equations In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation (Formula presented.), with v(x, t) = g(x, t), (Formula presented.) can be approximated uniformly by solutions of nonlocal problems of the form (Formula presented.), with (Formula presented.) , (Formula presented.) , as (Formula presented.) , for an appropriate rescaled kernel (Formula presented.). In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels, that is, (Formula presented.). © 2016, Springer International Publishing. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00442275_v67_n3_p_Molino http://hdl.handle.net/20.500.12110/paper_00442275_v67_n3_p_Molino
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Evolution problems
Nonlocal diffusion
Spacial dependence
Mathematical techniques
Dirichlet problem
Evolution problem
Nonlocal diffusion
Nonlocal problems
Parabolic Equations
Spacial dependence
Spatial dependence
Symmetric kernel
Partial differential equations
spellingShingle Evolution problems
Nonlocal diffusion
Spacial dependence
Mathematical techniques
Dirichlet problem
Evolution problem
Nonlocal diffusion
Nonlocal problems
Parabolic Equations
Spacial dependence
Spatial dependence
Symmetric kernel
Partial differential equations
Rossi, Julio Daniel
Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
topic_facet Evolution problems
Nonlocal diffusion
Spacial dependence
Mathematical techniques
Dirichlet problem
Evolution problem
Nonlocal diffusion
Nonlocal problems
Parabolic Equations
Spacial dependence
Spatial dependence
Symmetric kernel
Partial differential equations
description In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation (Formula presented.), with v(x, t) = g(x, t), (Formula presented.) can be approximated uniformly by solutions of nonlocal problems of the form (Formula presented.), with (Formula presented.) , (Formula presented.) , as (Formula presented.) , for an appropriate rescaled kernel (Formula presented.). In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels, that is, (Formula presented.). © 2016, Springer International Publishing.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
title_short Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
title_full Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
title_fullStr Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
title_full_unstemmed Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
title_sort nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00442275_v67_n3_p_Molino
http://hdl.handle.net/20.500.12110/paper_00442275_v67_n3_p_Molino
work_keys_str_mv AT rossijuliodaniel nonlocaldiffusionproblemsthatapproximateaparabolicequationwithspatialdependence
_version_ 1768543743678349312

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