On a solvability of contact problems with visco-plastic friction in the thermo-visco-plastic Bingham rheology

This paper deals with the solvability of contact problems with a local visco-plastic friction in the thermo-visco-plastic Bingham rheology. The generalized case of bodies of arbitrary shapes being in mutual contacts is investigated. The model problem represents mathematical models of the Earth’s mantle movements, of the volcanic zones, etc. Numerical approaches in the dynamic case, based on the semi-implicit scheme in time and a finite element approximation in the space, and in the stationary flow case, based on the penalization, regularization and finite element techniques and semi-implicit scheme in thermal part of the problem, are shortly developed and discussed.