THE INITIAL-VALUE PROBLEM FOR A SYSTEM MODELING UNIDIRECTIONAL LONGITUDINAL ELASTIC-PLASTIC WAVES

The authors analyze initial value problems for a hyperbolic system of equations that is a simplification of models of dynamic longitudinal e lastoplastic deformations in a rod with hardening. The simplified syst em has a positive characteristic speed associated with stress waves, a nd a zero speed associated with the time independence of hardening dur ing elastic deformation. The equations are piecewise linear in stress derivatives, and thus fully nonlinear. The main result is that for bou nded uniformly continuous initial data, the Cauchy problem has a uniqu e continuous solution that can be approximated by piecewise linear sol utions of the equations.