Roland Gachechiladze
abstract:
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.
Mathematics Subject Classification: 35J86, 49J40, 74M10, 74M15
Key words and phrases: Couple-stress elasticity theory, viscoelasticity, contact problem with friction, variational inequality, variational equation, Faedo-Galerkin method