Chapter 8 Introduction to Stefan-Type Problems

Abstract

The classical Stefan model is a free boundary problem that represents thermal processes in phase transitions just by accounting for heat-diffusion and exchange of latent heat. The weak and the classical formulations of the basic Stefan system, in one and in several dimensions of space, are here reviewed. The basic model is then improved by accounting for surface tension, for nonequilibrium, and dealing with phase transitions in binary composites, where both heat and mass diffuse. The existence of a weak solution is proved for the initial- and boundary-value problem associated to the basic Stefan model, and also for a problem with phase relaxation and nonlinear heat-diffusion. Some basic analytical notions are also briefly illustrated: convex calculus, maximal monotonicity, accretiveness, and others. © 2008 Elsevier B.V. All rights reserved.