Solvability of boundary value problems of the dynamics of nonlinear viscoelastic shells

The general initial-boundary value problem of the nonlinear theory of visco elastic shells of the Koiter type is considered in curvilinear coordinates. A generalized solution to the problem is defined on the basis of mechanica l variational principles. Two theorems on the existence of generalized solu tions in energy spaces are established. The results on existence are obtain ed by the application of the Faedo-Galerkin method.