Quasilinear Hyperbolic Systems with Involutions

The evolution of n-dimensional continuous media with elastic response is generally governed by quasilinear hyperbolic systems of partial differential equations $${artial _t}U + umimits_{lpha = 1}^m {{artial _lpha }} {G_lpha }(U) = 0$$ (1.1) which may express, as applicable, the conservation laws of mass, momentum, energy, electric charge, etc. Here x takes values in R m and ∂ α stands for the operator ∂/∂x α The state vector U takes values in an open subset O of R n and $${G_lpha }:arphi o {R^n},{ext{ }}lpha {ext{ = 1,}} dots ,m,$$ (1.2) are given, smooth, constitutive functions.