Travelling wave solutions to model equations of van der Waals fluids - Piechór, K. (Archives of Mechanics, 1996)
We consider the existence and uniqueness of travelling wave solutions to the model hydrodynamics equations (without capillarity) obtained from a four-velocity kinetic model of van der Waals fluids. We analyze both the Euler and the Navier-stokes equations. The Euler equations are shown to change their type. The Rankine-Hugoniot conditions are discussed in detail. It is shown that the Hugoniot locus can be disconnected even if the equations are hyperbolic. Using the Navier-stokes equations we show how to modify the Oleinik-Liu conditions of admissibility of shock waves to such situations. The shock-wave structures are found numerically. In particular, the so-called impending shock splitting is obtained.