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Abstract:

We study the following singular perturbation problem for a quasilinear uniformly parabolic operator of interest in combustion theory: div F(∇uε)-∂tuε = βε(uε), where uε ≥ 0, βε(s) = (1/ε)β(s/ε), ε > 0, β is Lipschitz continuous, supp β = [0, 1] and β > 0 in (0, 1). We obtain uniform estimates, we pass to the limit (ε → 0) and we show that, under suitable assumptions, the limit function u is a solution to the free boundary problem div F(∇u) - ∂tu = 0 in {u > 0}, uυ = α(υ, M) on ∂{u > 0}, in a pointwise sense and in a viscosity sense. Here uυ denotes the derivative of u with respect to the inward unit spatial normal υ to the free boundary ∂{u > 0}, M = ∫ β(s) ds, α(υ, M) := Φv -1 (M) and Φv(α) := - A(αυ) +αυ · F(αυ), where A(p) is such that F(p) = ∇A(p) with A(0) = 0. Some of the results obtained are new even when the operator under consideration is linear. © European Mathematical Society 2008.

Registro:

Documento: Artículo
Título:A quasilinear parabolic singular perturbation problem
Autor:Lederman, C.; Oelz, D.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Faculty of Mathematics, Vienna University, Nordbergstr. 15, A 1090 Wien, Austria
Palabras clave:Combustion; Free boundary problem; Quasilinear parabolic operator; Singular perturbation problem
Año:2008
Volumen:10
Número:4
Página de inicio:447
Página de fin:482
DOI: http://dx.doi.org/10.4171/IFB/197
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_v10_n4_p447_Lederman

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Citas:

---------- APA ----------
Lederman, C. & Oelz, D. (2008) . A quasilinear parabolic singular perturbation problem. Interfaces and Free Boundaries, 10(4), 447-482.
http://dx.doi.org/10.4171/IFB/197
---------- CHICAGO ----------
Lederman, C., Oelz, D. "A quasilinear parabolic singular perturbation problem" . Interfaces and Free Boundaries 10, no. 4 (2008) : 447-482.
http://dx.doi.org/10.4171/IFB/197
---------- MLA ----------
Lederman, C., Oelz, D. "A quasilinear parabolic singular perturbation problem" . Interfaces and Free Boundaries, vol. 10, no. 4, 2008, pp. 447-482.
http://dx.doi.org/10.4171/IFB/197
---------- VANCOUVER ----------
Lederman, C., Oelz, D. A quasilinear parabolic singular perturbation problem. Interfaces Free Boundaries. 2008;10(4):447-482.
http://dx.doi.org/10.4171/IFB/197