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 is a solution to the free boundary problem in , on , in a pointwise sense and in a viscosity sense. Here is the inward unit spatial normal to the free boundary and is a positive constant. Some of the results obtained are new even when the operator under consideration is linear.
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Claudia Lederman, Dietmar Oelz, A quasilinear parabolic singular perturbation problem. Interfaces Free Bound. 10 (2008), no. 4, pp. 447–482DOI 10.4171/IFB/197