Riemann problems for a class of coupled hyperbolic systems of conservation laws

Abstract

We study a class of coupled hyperbolic systems of conservation laws which contain the one-dimensional zero-pressure gas dynamics as a prototypical example. The Riemann problems are solved constructively. The Riemann solutions exactly include two kinds: delta-shock wave solutions and vacuum solutions. Under the generalized Rankine-Hugoniot relation and entropy condition, all of the existence, uniqueness, and stability of solutions to viscous perturbations are proved. Two typical examples are presented finally. © 1999 Academic Press.