Convexity and uniqueness in a free boundary problem arising in combustion theory.

Título inglés	Convexity and uniqueness in a free boundary problem arising in combustion theory.
Título español	Convexidad y unicidad en un problema de frontera libre que surge en la teoría de la combustión.
Autor/es	Petrosyan, Arshak
Organización	Dep. Math. Univ. Texas Austin, Austin (Texas), Estados Unidos
Revista	0213-2230
Publicación	2001, 17 (3): 421-431, 12 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω Ì QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such that ut = Δu,    in Ω, u = 0 and |Ñu| = 1,   on Γ := ∂Ω ∩ QT, u(·,0) = u0,     on Ω0, where Ω0 is a given domain in Rn and u0 is a positive and continuous function in Ω0, vanishing on ∂Ω0. If Ω0 is convex and u0 is concave in Ω0, then we show that (u,Ω) is unique and the time sections Ωt are convex for every t Î (0,T), provided the free boundary Γ is locally the graph of a Lipschitz function and the fixed gradient condition is understood in the classical sense.
Clasificación UNESCO	120220
Palabras clave español	Problema de Dirichlet ; Condiciones de contorno ; Dominios convexos ; Dominios de Lipschitz ; Unicidad ; Ecuación del calor
Código MathReviews	MR1900891
Código Z-Math	Zbl 1027.35165
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