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