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

Revista Matemática Iberoamericana (2001)

- Volume: 17, Issue: 3, page 421-431
- ISSN: 0213-2230

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topPetrosyan, Arshak. "Convexity and uniqueness in a free boundary problem arising in combustion theory.." Revista Matemática Iberoamericana 17.3 (2001): 421-431. <http://eudml.org/doc/39654>.

@article{Petrosyan2001,

abstract = {We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such thatut = Δu, in Ω,u = 0 and |∇u| = 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 ∈ (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.},

author = {Petrosyan, Arshak},

journal = {Revista Matemática Iberoamericana},

keywords = {Problema de Dirichlet; Condiciones de contorno; Dominios convexos; Dominios de Lipschitz; Unicidad; Ecuación del calor; heat equation; propagation of flames; gradient condition},

language = {eng},

number = {3},

pages = {421-431},

title = {Convexity and uniqueness in a free boundary problem arising in combustion theory.},

url = {http://eudml.org/doc/39654},

volume = {17},

year = {2001},

}

TY - JOUR

AU - Petrosyan, Arshak

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

JO - Revista Matemática Iberoamericana

PY - 2001

VL - 17

IS - 3

SP - 421

EP - 431

AB - We consider solutions to a free boundary problem for the heat equation, describing the propagation of flames. Suppose there is a bounded domain Ω ⊂ QT = Rn x (0,T) for some T > 0 and a function u > 0 in Ω such thatut = Δu, in Ω,u = 0 and |∇u| = 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 ∈ (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.

LA - eng

KW - Problema de Dirichlet; Condiciones de contorno; Dominios convexos; Dominios de Lipschitz; Unicidad; Ecuación del calor; heat equation; propagation of flames; gradient condition

UR - http://eudml.org/doc/39654

ER -

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