A free-boundary problem in combustion theory
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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2000
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder http://hdl.handle.net/20.500.12110/paper_14639963_v2_n4_p381_Bonder |
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paper:paper_14639963_v2_n4_p381_Bonder2023-06-08T16:16:39Z A free-boundary problem in combustion theory 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. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder http://hdl.handle.net/20.500.12110/paper_14639963_v2_n4_p381_Bonder |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| title |
A free-boundary problem in combustion theory |
| spellingShingle |
A free-boundary problem in combustion theory |
| title_short |
A free-boundary problem in combustion theory |
| title_full |
A free-boundary problem in combustion theory |
| title_fullStr |
A free-boundary problem in combustion theory |
| title_full_unstemmed |
A free-boundary problem in combustion theory |
| title_sort |
free-boundary problem in combustion theory |
| publishDate |
2000 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v2_n4_p381_Bonder http://hdl.handle.net/20.500.12110/paper_14639963_v2_n4_p381_Bonder |
| _version_ |
1768544054259220480 |