Geodesic
A quasilinear parabolic singular perturbation problem
Claudia Lederman1 ; Dietmar Oelz2
1Universidad de Buenos Aires, Argentina
2Universität Wien, Austria
Interfaces and free boundaries, Tome 10 (2008) no. 4, pp. 447-482

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DOI

We study a singular perturbation problem for a quasilinear uniformly parabolic operator of interest in combustion theory. We obtain uniform estimates, we pass to the limit and we show that, under suitable assumptions, the limit function u is a solution to the free boundary problem divF(∇u)−∂t​u=0 in {u>0}, uν​=α(ν,M) on ∂{u>0}, in a pointwise sense and in a viscosity sense. Here ν is the inward unit spatial normal to the free boundary ∂{u>0} and M is a positive constant. Some of the results obtained are new even when the operator under consideration is linear.
DOI : 10.4171/ifb/197
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Quasilinear parabolic operator, singular perturbation problem, free boundary problem, combustion

Claudia Lederman  1   ; Dietmar Oelz  2

1 Universidad de Buenos Aires, Argentina
2 Universität Wien, Austria 
Claudia Lederman; Dietmar Oelz. A quasilinear parabolic singular perturbation problem. Interfaces and free boundaries, Tome 10 (2008) no. 4, pp. 447-482. doi: 10.4171/ifb/197
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     title = {A quasilinear parabolic singular perturbation problem},
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     year = {2008},
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     number = {4},
     doi = {10.4171/ifb/197},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/197/}
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