The unsteady linearized model of movement of the incompressible viscoelastic liquid of high order

The author considers the first initial boundary-value problem for the Oskolkov equation system modeling the dynamics of the incompressible viscoelastic liquid of Kelvin - Voight of high order in the linear approximation. This problem is solved within the frameworks of the theory of the linear heterogeneous Sobolev type equations. The author proves the existence theorem of the unique solution of the problem and finds the description of its extended phase space.