ABSTRACT
The goal of this paper is to attempt to extend Lax's idea to a form which is amenable to mixed problems as well, e.g. the dynamics of a van der Waals fluid. Specifically, They compare shocks obtained by the Lax-Friedrichs scheme with those permitted by the viscosity-capillarity criterion. In this chapter, the author considers shock structure problems for an isothermal compressible fluid in Lagrangian coordinates. They derive analogous results for Eulerian coordinates. Unfortunately, as is also well known, weak solutions for quasi-linear hyperbolic equations are notoriously non-unique. In the first two sections the authors considered shock structure problems for an isothermal compressible fluid in Lagrangian coordinates. They derive analogous results for Eulerian coordinates.
