Some Existence Theorems for ann-Dimensional Parabolic Equation with a Discontinuous Source Term

Abstract

The authors consider an n-dimensional semilinear equation of parabolic type with a discontinuous source term arising from combustion theory. The authors prove a local existence for a classical solution having a “regular” free boundary. In this regard, the free boundary is a surface through which the discontinuous source term exhibits a switch-like behaviour. The authors specify conditions under which this solution and its free boundary are global in time. The authors also prove uniqueness and continuous dependence theorems.