On the nonuniqueness of solutions of the equations of the non-linear theory of elasticity

The system of equations of the non-linear theory of elasticity, which is a hyperbolic system expressing the laws of conservation of mass, momentum, and energy, describes both continuous and discontinuous solutions.
Self-similar problems: the problem of disintegration of an arbitrary discontinuity and the ‘piston problem’. Non-uniqueness of the solutions of these problems. Passage to the linear limit as the amplitude of the perturbations tends to zero. Metastable shock wave — the cause of non-uniqueness? Its stability with respect to small perturbations.
Visco-elastic media. Structure of shock waves. Numerical experiments in problems with nonviscous self-similar asymptotics; under suitable conditions any of the non-viscous solutions can be realized as the asymptotic behaviour. Non-linear stability of metastable shock waves.
Concluding remarks. Influence of dispersion on the properties of shock waves.