Artículo
Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | A free-boundary problem in combustion theory |
| Autor: | Bonder, J.F.; Wolanski, N. |
| Filiación: | Departamento de Matemática, FCEyN, UBA, Buenos Aires, 1428, Argentina |
| Año: | 2000 |
| Volumen: | 2 |
| Número: | 4 |
| Página de inicio: | 381 |
| Página de fin: | 411 |
| Título revista: | Interfaces and Free Boundaries |
| Título revista abreviado: | Interfaces Free Boundaries |
| ISSN: | 14639963 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder |
Referencias:
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- 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
- Buckmaster, J.D., Ludford, G.S.S., (1982) Theory of Laminar Flames, , Cambridge University Press, Cambridge
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- 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
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- Lederman, C., Vazquez, J.L., Wolanski, N., Uniqueness of solution in a free boundary problem from combustion Trans AMS, , to appear
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Citas:
---------- APA ----------
Bonder, J.F. & Wolanski, N. (2000) . A free-boundary problem in combustion theory. Interfaces and Free Boundaries, 2(4), 381-411.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder [ ]
---------- CHICAGO ----------
Bonder, J.F., Wolanski, N. "A free-boundary problem in combustion theory" . Interfaces and Free Boundaries 2, no. 4 (2000) : 381-411.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder [ ]
---------- MLA ----------
Bonder, J.F., Wolanski, N. "A free-boundary problem in combustion theory" . Interfaces and Free Boundaries, vol. 2, no. 4, 2000, pp. 381-411.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder [ ]
---------- VANCOUVER ----------
Bonder, J.F., Wolanski, N. A free-boundary problem in combustion theory. Interfaces Free Boundaries. 2000;2(4):381-411.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder [ ]
