A free-boundary problem in combustion theory

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In this paper we consider the following problem arising in combustion theory: (Equation presented) where D ∪ ℝN+1, fϵ(s)1/ϵ2f (s/ϵ) with f a Lipschitz continuous function with support in (-∞,1] Here νϵ is the mass fraction of some reactant, uϵ the rescaled temperature of the mixture and ϵ is essenti...

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Detalles Bibliográficos
Autor principal: Bonder, J.F
Otros Autores: Wolanski, N.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: European Mathematical Society Publishing House 2000
Acceso en línea:Registro en Scopus
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100 1 |a Bonder, J.F. 
245 1 2 |a A free-boundary problem in combustion theory 
260 |b European Mathematical Society Publishing House  |c 2000 
506 |2 openaire  |e Política editorial 
504 |a Athanasopoulos, I., Caffarelli, L.A., Salsa, S., Caloric functions in Lipschitz domains and the regularity of solutions to phase transitions problems (1996) Ann. Math, 143, pp. 413-434 
504 |a Berestycki, H., Caffarelli, L.A., Nirenberg, L., Uniform estimates for regularization of free boundary problems (1988) Annal. and Partial Diff. Eq., Lecture Notes in Pure and Applied Mathematics, 122. , SADOSKY, C. ed, Marcel Dekker 
504 |a Buckmaster, J.D., Ludford, G.S.S., (1982) Theory of Laminar Flames, , Cambridge University Press, Cambridge 
504 |a Caffarelli, L.A., Uniform Lipschitz regularity of a singular perturbation problem (1995) Diff. and Int. Eq., 8, pp. 1585-1590 
504 |a Caffarelli, L.A., Lederman, C., Wolanski, N., Uniform estimates and limits for a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J, 46, pp. 453-490 
504 |a Caffarelli, L.A., Lederman, C., Wolanski, N., Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem (1997) Indiana Univ. Math. J, 46, pp. 719-740 
504 |a Caffarelli, L.A., Vázquez, J.L., A free boundary problem for the heat equation arising in flame propagation (1995) Trans Am. Math. Soc, 347, pp. 411-441 
504 |a Fornari, L., Regularity of the Solution and of the Free Boundary for Free Boundary Problems Arising in Combustion Theory, , Preprint 
504 |a Ladyzhenskaya, O.A., Solonnikov, V.A., Ural'Ceva, N.N., Linear and quasilinear equations of parabolic type (1968) Transl. Math. Monographs, 23. , American Mathematical Society, Providence R. I 
504 |a Lederman, C., Vazquez, J.L., Wolanski, N., Uniqueness of solution in a free boundary problem from combustion Trans AMS, , to appear 
504 |a Lederman, C., Vazquez, J.L., Wolanski, N., Uniqueness of Solution to a Two Phase Free Boundary Problem, , Preprint 
504 |a Lederman, C., Wolanski, N., Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem (1998) Analli della Scuola Normale Sup. Pisa. Ser. IV, 27, pp. 253-288. , Fasc. 2 
504 |a Zeldovich, Ya.B., Frank-Kamenetski, D.A., The theory of thermal propagation of flames (1938) Zh. Fiz. Khim, 12, pp. 100-105. , Russian 
504 |a (1992) Collected Works of Ya. B. Zeldovich, 1. , Princeton Univ. Press 
520 3 |a In this paper we consider the following problem arising in combustion theory: (Equation presented) where D ∪ ℝN+1, fϵ(s)1/ϵ2f (s/ϵ) with f a Lipschitz continuous function with support in (-∞,1] Here νϵ is the mass fraction of some reactant, uϵ the rescaled temperature of the mixture and ϵ is essentially the inverse of the activation energy. This model is derived in the framework of the theory of equi-diffusional premixed flames for Lewis number 1. We prove that, under suitable assumptions on the functions uϵ and νϵ, we can pass to the limit (ϵ → 0).the so-called high-activation energy limit.and that the limit function u = lim uϵ = lim νϵ is a solution of the following free-boundary problem: (Equation presented) in a pointwise sense at regular free-boundary points and in a viscosity sense. Here M(x, t) = f1-w0(x, t)(s + w0(x, t)) f (s) ds and -1 < w0 = limϵ-0 νϵ-uϵ/ϵ. Since νϵ-uϵ is a solution of the heat equation, it is fully determined by its initial-boundary datum. in particular, the free-boundary condition only (but strongly) depends on the approximation of the initial-boundary datum. Moreover, if D ⊂ ∂{u > 0} is a Lipschitz surface, u is a classical solution to (0.1). © Oxford University Press 2000.  |l eng 
536 |a Detalles de la financiación: Universidad de Buenos Aires, TX47 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, 03-00000-00137, PICT No., CONICET PIP0660/98 
536 |a Detalles de la financiación: J. F. Bonder is grateful to J. D. Rossi for his constant support and several interesting discussions. This work was partially supported by Universidad de Buenos Aires under grant TX47, by ANPCyT PICT No. 03-00000-00137 and CONICET PIP0660/98. N. I. Wolanski is a member of CONICET. 
593 |a Departamento de Matemática, FCEyN, UBA, Buenos Aires, 1428, Argentina 
700 1 |a Wolanski, N. 
773 0 |d European Mathematical Society Publishing House, 2000  |g v. 2  |h pp. 381-411  |k n. 4  |p Interfaces Free Boundaries  |x 14639963  |t Interfaces and Free Boundaries 
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