Existence and approximation of solutions to an anisotropic phase field system for the kinetics of phase transitions (Q1599130)

Summary: This paper is concerned with a phase field system of Penrose-Fife type \[ c_0\theta_t+ \lambda'(\chi) \chi_t+\nabla\vec q=g, \quad \vec q=\kappa (\theta)\nabla \left({1\over \theta}\right), \] \[ \zeta(\nabla \chi)\chi_t- \varepsilon \Delta_\chi+ s'(\chi)= -{\lambda'(\chi) \over \theta} \] for a nonconserved-order parameter \(\chi\) with a kinetic relaxation coefficient \(\zeta\) 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.