DYNAMICAL CONTACT PROBLEMS WITH REGARD TO FRICTION OF COUPLE-STRESS VISCOELASTICITY FOR INHOMOGENEOUS ANISOTROPIC BODIES

摘要

The paper deals with the three-dimensional boundary-contact problems of couple-stress viscoelasticity for inhomogeneous anisotropic bodies with friction. The uniqueness theorem is proved by using the corresponding Green’s formulas and positive definiteness of the potential energy. To analyze the existence of solutions, the problem under consideration is reduced equivalently to a spatial variational inequality. A special parameter-dependent regularization of this variational inequality is considered, which is equivalent to the relevant regularized variational equation depending on a real parameter, and its solvability is studied by the Faedo–Galerkin method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure the existence theorem for the original contact problem with friction is proved.