This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.
A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation, which is a system of ordinary equations, the global solution which includes delta-shock waves and vacuum is constructed.
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