Non existence of shock structure solutions for hyperbolic dissipative systems including characteristic shocks

Abstract

We discuss shock wave structure solutions of a general dissipative quasi-linear hyperbolic system of balance laws. For boundary conditions corresponding to Lax shocks we prove that an upper bound exists such that for a shock velocity greater than this limit C1 solutions cannot exist. Moreover for boundary conditions corresponding to a characteristic shock, there are not continuous solutions also if the shock is weak. The examples of non equilibrium thermodynamics for monoatomic fluids are included.

Keywords:

• shocks
• shock shucture
• hyperbolic systems