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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| Autores principales: | , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_14639963_v2_n4_p381_Bonder |
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| Sumario: | 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. |
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