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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Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman |
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todo:paper_03605302_v31_n2_p195_Lederman2023-10-03T15:26:36Z Singular perturbation in a nonlocal diffusion problem Lederman, C. Wolanski, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 |
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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, C. Wolanski, N. 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. |
format |
JOUR |
author |
Lederman, C. Wolanski, N. |
author_facet |
Lederman, C. Wolanski, N. |
author_sort |
Lederman, C. |
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 |
url |
http://hdl.handle.net/20.500.12110/paper_03605302_v31_n2_p195_Lederman |
work_keys_str_mv |
AT ledermanc singularperturbationinanonlocaldiffusionproblem AT wolanskin singularperturbationinanonlocaldiffusionproblem |
_version_ |
1782024117973680128 |