Existence and approximation of solutions to an anisotropic phase field system for the kinetics of phase transitions

This paper is concerned with a phase field system of Penrose-Fife type for a non-conserved order parameter with a kinetic relaxation coefficient depending on the gradient of the order parameter. This system can be used to model the anisotropic solidification of liquids. A time-discrete scheme for an initial-boundary value problem to this system is presented. By proving the convergence of this scheme, the existence of a solution to the problem is shown