# A quasilinear parabolic singular perturbation problem

### Claudia Lederman

Universidad de Buenos Aires, Argentina### Dietmar Oelz

Universität Wien, Austria

## 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 $divF(∇u)−∂_{t}u=0$ in ${u>0}$, $u_{ν}=α(ν,M)$ 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.

## Cite this article

Claudia Lederman, Dietmar Oelz, A quasilinear parabolic singular perturbation problem. Interfaces Free Bound. 10 (2008), no. 4, pp. 447–482

DOI 10.4171/IFB/197