Siberian Federal University

The complete system of equations for the dynamics of a Cosserat-type continuum with couple stresses under finite strains and particle rotations in Lagrangian variables is reduced to a compatible system of conservation laws in the Godunov sense. This system enables analyzing generalized solutions with surfaces of strong discontinuity of stresses and velocities and allows integral estimates that guarantee the uniqueness and continuous dependence of solutions of the Cauchy problem and boundary-value problems with dissipative boundary conditions on the initial data