Breakdown of shock-wave-structure solutions.

We determine, for a generic dissipative hyperbolic system of balance laws, an upper bound such that for shock velocity greater than this limit no continuous shock-wave-structure solutions may exist. These general results are applied to the old and open problem of shock waves in classical and relativistic nonequilibrium thermodynamics. In this context, for the macroscopic theories of the extended thermodynamics related to the moment Grad procedure for the Boltzmann equation we can prove that this upper bound for critical Mach numbers is not influenced by adding other nonlinear terms