The formulation of generalized transport laws leading to causal hyperbolic hydrodynamical equations gives rise to a critical Mach number ${\mathit{M}}_{\mathit{c}}$ at which a singularity develops in the shock wave layer. This happens in kinetic theory of gases (Grad’s 13 moments method) and extended irreversible thermodynamics as well. In this paper, it is shown that if nonlinear and nonlocal effects are taken into account, ${\mathit{M}}_{\mathit{c}}$ significantly increases. Specifically, nonlocal effects raise ${\mathit{M}}_{\mathit{c}}$ from 2.01 up to 3.03. Further consideration of some nonlinear terms raise ${\mathit{M}}_{\mathit{c}}$ from the latter value up to 4.67.

• Received 29 April 1991

DOI:https://doi.org/10.1103/PhysRevA.44.6496