On the influence of viscosity on Riemann solutions (Q1382714)

This paper is a study of traveling waves for \(2\times 2\) systems of conservation laws that change type, with added viscous terms. Using the framework of the fundamental wave manifold, the author systematically analyzes vector fields whose separatrices represent traveling waves. Various bifurcations are identified, and the resulting changes in structure of admissible and inadmissible shock wave solutions of the underlying conservation laws are incorporated into the construction of solutions of Riemann problems. This leads to an analysis of surfaces across which the number of admissible solutions of Riemann problems changes.