Global continuous Riemann solver for nonlinear elasticity

We consider in this paper an isothermal model of nonlinear elasticity. This model is described by two conservation laws that define a problem of mixed type, both elliptic and hyperbolic. We restrict ourselves to the linearly degenerate case, and consider Riemann data that lies in the hyperbolic regi ons. The lack of uniqueness of the Riemann problem is solved by the introdu ction of a so-called kinetic relation, used to narrow the set of admissible subsonic phase transitions. In this situation, we consider the Riemann pro blem for any data lying in the hyperbolic region, using either explicit com putations or geometric arguments. This construction allows us to give suffi cient conditions on the kinetic relation in order that the generated Rieman n solver possesses properties of uniqueness, globality, and continuous depe ndence on the initial data in the L-1 distance.