Singular perturbation in a nonlocal diffusion problem

We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solu...

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Autores principales: Lederman, Claudia Beatriz, Wolanski, Noemi Irene
Publicado: 2006
Materias:
Combustion
Free boundary problem
Nonlocal diffusion
Nonlocal evolution operator
Viscosity solutions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v31_n2_p195_Lederman
http://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03605302_v31_n2_p195_Lederman
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spelling paper:paper_03605302_v31_n2_p195_Lederman2023-06-08T15:34:48Z Singular perturbation in a nonlocal diffusion problem Lederman, Claudia Beatriz Wolanski, Noemi Irene Combustion Free boundary problem Nonlocal diffusion Nonlocal evolution operator Viscosity solutions We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free boundary points. We study the nonlocal problem both for a single equation and for a system of two equations. Some of the results obtained are new even when the operator under consideration is the heat operator. Fil:Lederman, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v31_n2_p195_Lederman http://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Combustion
Free boundary problem
Nonlocal diffusion
Nonlocal evolution operator
Viscosity solutions
spellingShingle Combustion
Free boundary problem
Nonlocal diffusion
Nonlocal evolution operator
Viscosity solutions
Lederman, Claudia Beatriz
Wolanski, Noemi Irene
Singular perturbation in a nonlocal diffusion problem
topic_facet Combustion
Free boundary problem
Nonlocal diffusion
Nonlocal evolution operator
Viscosity solutions
description We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free boundary points. We study the nonlocal problem both for a single equation and for a system of two equations. Some of the results obtained are new even when the operator under consideration is the heat operator.
author Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_sort Lederman, Claudia Beatriz
title Singular perturbation in a nonlocal diffusion problem
title_short Singular perturbation in a nonlocal diffusion problem
title_full Singular perturbation in a nonlocal diffusion problem
title_fullStr Singular perturbation in a nonlocal diffusion problem
title_full_unstemmed Singular perturbation in a nonlocal diffusion problem
title_sort singular perturbation in a nonlocal diffusion problem
publishDate 2006
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v31_n2_p195_Lederman
http://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman
work_keys_str_mv AT ledermanclaudiabeatriz singularperturbationinanonlocaldiffusionproblem
AT wolanskinoemiirene singularperturbationinanonlocaldiffusionproblem
_version_ 1768546398965334016

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