On a coupled Stefan-like problem in thermo-visco-plastic rheology (Q1372095)

The paper deals with coupled Stefan-like problems arising in thermo-viscoplastic rheology. The physical model is derived by using conservation principles. The author gives the existence of weak solutions by means of the regularization of nonlinear degenerate terms and uses a nondifferentiable functional arising in variational formulation of the problem. The model investigated represents geodynamic processes in the Earth and describes critical situations in regions, where high-level radioactive waste disposal systems will be situated. A sequence of regularized solutions is obtained by Galerkin approximations and monotonicity arguments.