Abstract: We discuss results on the structural stability of shock waves in elastodynamics of compressible neo-Hooken materials. By nonlinear structural stability of a shock wave we mean the local-in-time existence and uniqueness of the discontinuous shock front solution to the corresponding system of hyperbolic conservation laws. We describe finding structural stability conditions for shock waves in 2D elastodynamics by both the energy method and the spectral analysis of the corresponding linearized problem. We also briefly discuss recent results on the structural stability in the general 3D case.
