| In recent times there has been a resurgence of research in the study of the regularity of two phase free boundary problems, especially in the difficult parabolic case. These problems are often approximated by regularizing ones. To obtain information about the solution to the original problem one tries to establish results for the approximating ones which carry over in the limit. In this work I will discuss the uniform properties of the a two phase parabolic singular perturbation problem. In particular, my main objective is to show that, under suitable assumptions, it is an approximation for a free boundary problem that naturally arises in combustion theory in the analysis of the propagation of curved flames in non-homogeneous media, specifically in the description of laminar flames as an asymptotic limit for high activation energy. |
