Existence theorems for a free boundary problem in combustion theory

This paper analyzes a one-dimensional parabolic partial differential equation which models a large number of physical phenomena. These are phenomena which, viewed on an appropriate time scale, exhibit a switch-like behavior. For this reason there is a source term in the equation that is discontinuous as a function of the dependent variable with a jump discontinuity. The aim of this paper is to prove a global existence theorem of a classical solution having a ″regular″ free boundary, a curve which separates the domain in which the problem is studies into two regions and through which the source term exhibits a jump.