Structures of longitudinal-torsional shock waves and special discontinuities in nonlinearly viscoelastic media with dispersion

Weakly nonlinear longitudinal-torsional waves in rods are considered. The structure of discontinuities in the solutions of the hyperbolic system of equations describing these waves is studied. Previously, the authors studied discontinuity structures under more special assumptions about dissipative processes in these structures. In the present study, no constraints are imposed on the matrix of dissipative coefficients except for positive definiteness. Conditions are formulated for the existence of special discontinuities, that is, discontinuities with additional boundary conditions that are independent of conservation laws.