Abstract
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 {\rm div } F(\nabla u)-\partial_{t}u=0 in \{ u>0 \} , u_\nu=\alpha(\nu, M) on \partial\{ u>0 \} , in a pointwise sense and in a viscosity sense. Here \nu is the inward unit spatial normal to the free boundary \partial\{ u>0 \} and M is a positive constant. Some of the results obtained are new even when the operator under consideration is linear.
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