Nonlocal and nonlinear effects in shock waves

The formulation of generalized transport laws leading to causal hyperbolic hydrodynamical equations gives rise to a critical Mach number Mc 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, Mc significantly increases. Specifically, nonlocal effects raise Mc from 2.01 up to 3.03. Further consideration of some nonlinear terms raise Mc from the latter value up to 4.67.