One and two phase Stefan problems for the linear heat equation have been the subject of many studies in the past [1, 2]. Indeed these problems have a great physical relevance since they provide a mathematical model for the processes of phase changes [3, 4]. The boundary between the two phases is a free boundary: its motion has to be determined as part of the solution. More recently the previous...

An approximation procedure for the identiication of a nonlinear boundary heat transfer function in a one phase Stefan problem is presented. Alternatively the problem can be viewed as constructing a feedback control law for the control of the solidiication surface in the Stefan problem. The analysis is based on Hilbert space methods and convex analysis techniques. Numerical results combining two...

In this paper we generalize the degenerate two{phase Stefan problem (Mullins{ Sekerka evolution) to multi{phase systems. We prove a conditional existence result for this evolution problem in the framework of geometric measure theory by using an implicit time discretization. In each time step we solve a variational problem for an energy functional that contains capillarity terms as well as bulk ...

The well posedness of the two-phase Stefan problem with convection is established in $$L^{1}$$ . First we consider case a singular enthalpy and fix velocity. In second part paper study smoothed enthalpy, but velocity solution to Navier-Stokes equation. last section give some numerical illustrations physical simulated using models studied paper.