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Abstract:

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.

Registro:

Documento: Artículo
Título:Singular perturbation in a nonlocal diffusion problem
Autor:Lederman, C.; Wolanski, N.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Combustion; Free boundary problem; Nonlocal diffusion; Nonlocal evolution operator; Viscosity solutions
Año:2006
Volumen:31
Número:2
Página de inicio:195
Página de fin:241
DOI: http://dx.doi.org/10.1080/03605300500358111
Título revista:Communications in Partial Differential Equations
Título revista abreviado:Commun. Partial Differ. Equ.
ISSN:03605302
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03605302_v31_n2_p195_Lederman

Referencias:

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Citas:

---------- APA ----------
Lederman, C. & Wolanski, N. (2006) . Singular perturbation in a nonlocal diffusion problem. Communications in Partial Differential Equations, 31(2), 195-241.
http://dx.doi.org/10.1080/03605300500358111
---------- CHICAGO ----------
Lederman, C., Wolanski, N. "Singular perturbation in a nonlocal diffusion problem" . Communications in Partial Differential Equations 31, no. 2 (2006) : 195-241.
http://dx.doi.org/10.1080/03605300500358111
---------- MLA ----------
Lederman, C., Wolanski, N. "Singular perturbation in a nonlocal diffusion problem" . Communications in Partial Differential Equations, vol. 31, no. 2, 2006, pp. 195-241.
http://dx.doi.org/10.1080/03605300500358111
---------- VANCOUVER ----------
Lederman, C., Wolanski, N. Singular perturbation in a nonlocal diffusion problem. Commun. Partial Differ. Equ. 2006;31(2):195-241.
http://dx.doi.org/10.1080/03605300500358111