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...

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...

One proves that the moving interface of a two-phase Stefan problem on Ω⊂Rd, d=1,2,3, is controllable at end time T by Neumann boundary controller u. The phase-transition region mushy {σtu;0≤t≤T} modified and main result amounts to saying that, for each Lebesgue measurable set Ω∗ with positive measure, there u∈L2((0,T)×∂Ω) such Ω∗⊂σTu. To this aim, one uses an optimal control approach combined C...

We study a nonlocal version of the one-phase Stefan problem which develops mushy regions, even if they were not present initially, a model which can be of interest at the mesoscopic scale. The equation involves a convolution with a compactly supported kernel. The created mushy regions have the size of the support of this kernel. If the kernel is suitably rescaled, such regions disappear and the...

Abstract. The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modified Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A finite element method for discretization of the Stef...