We show the boundary controllability to stationary states of Stefan problem with two phases and in one dimension space variable. In case an initial condition that is a state for time control large enough, we also obtain sign constraints associated problem. Our method based on flatness approach consists writing solution controls through outputs their derivatives. construct these as Gevrey functi...

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...