Artículo
Uniqueness of solution to a free boundary problem from combustion
Fecha de publicación:
04/2001
Editorial:
American Mathematical Society
Revista:
Transactions of the American Mathematical Society
ISSN:
0002-9947
e-ISSN:
1088-6850
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, defined in a domain D ⊂ RN × (0, T) and such that ∆u +Xai uxi − ut = 0 in D∩{u > 0}. We also assume that the interior boundary of the positivity set, D ∩ ∂{u > 0}, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied: u = 0, −∂u/∂ν = C. Here ν denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Lederman, Claudia Beatriz; Vázquez, Juan Luis; Wolanski, Noemi Irene; Uniqueness of solution to a free boundary problem from combustion; American Mathematical Society; Transactions of the American Mathematical Society; 353; 2; 4-2001; 655-692
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