We consider one-dimensional two-phase Stefan problems for a finite substance with different boundary conditions at the fixed faces. The goal of this paper is to determine the behavior of the free boundary and the temperature when the thermal coefficients of the material change. We obtain properties of monotony with respect to the latent heat, the common mass density, the specific heat of each p...

We characterize the equilibrium states for the two-phase Stefan problem with surface tension and with or without kinetic undercooling, and we analyze their stability in dependence of physical and geometric quantities.

In this paper we study an initial{boundary value Stefan{type problem with phase relaxation where the heat ux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose{Fife model for diiusive phase transitions with non{conserved order parameter if the coeecient of the interfacial energy is taken as zero. It is shown that th...

This paper reformulates the two–phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamically consistent treatment of the interface conditions in the presence of a contact point involving ...