On a coupled Stefan-like problem in thermo-visco-plastic rheology

This paper is a study of the existence of solutions of Stefan-like problems describing solidification and melting of rock and metallic alloys. The governing equations are derived and the model problem is given. The main result represents the existence theorem. The proof proceeds by a regularization of the nonlinear degenerated terms and of the nondifferentiable functional j(.). Sequences of regularized solutions are obtained by the Galerkin approximations. For proving the solution monotonicity arguments are used. The problem investigated represents the model problem of solidification and melting as well as simulation of geodynamic processes in the Earth and simulation of critical situations (e.g. explosions of HLRWDSs) in regions, where high-level radioactive waste disposal systems (HLRWDSs) will be situated.