# Current Progress in Hyperbolic Systems: Riemann Problems and Computations

Share this page *Edited by *
*Barbara L. Keyfitz*

The study of Riemann problems has undergone a strong, steady
growth in the last decade. The general direction of the research has
headed toward understanding the wave structure of the solutions of
more physically realistic systems. These systems fail either or both
of the two main restrictions of the classical theory—that the
system be strictly hyperbolic or genuinely nonlinear. The systems that
have been studied tend to fall into the following broad classes: real
gas dynamics (including combustion), visco-elastic materials, phase
transitions, and multiphase flow in porous media. In addition to their
usefulness in large-scale calculations, computational schemes have
vastly improved the handling of discontinuity behavior.

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer
Research Conference on Current Progress in Hyperbolic Systems: Riemann Problems
and Computations, held at Bowdoin College in July 1988. The papers presented
here provide a complete picture of recent research by some of the leaders in
this field. Graduate students and beginning researchers will find this book a
useful introduction to current work in this area.

# Table of Contents

## Current Progress in Hyperbolic Systems: Riemann Problems and Computations

- Contents ix10 free
- Preface xi12 free
- Shock wave solutions of the 1d Navier-Stokes equations for compressible, isentropic flow 114 free
- Embedded hyperbolic regions in a nonlinear model for viscoelastic flow 922
- Capillary energy and the entropy condition for the Buckley-Leverett equation 2134
- Nonlinear elastoplastic waves 2740
- An example of a Riemann problem of second kind 5568
- Density profiles for diverging detonations 6376
- Anomalous waves in shock wave - fluid interface collisions 7790
- Time-dependent shear flow of a non-Newtonian fluid 91104
- The Riemann problem for combustion 111124
- Transitional shock waves 125138
- Three-phase flow with gravity 147160
- A system of conservation laws with a parabolic degeneracy 161174
- Nonlinear surface waves 185198
- A criterion for certain wave structures in systems that change type 203216
- A note on the stability of eigenvalue degeneracy in nonlinear conservation laws of multiphase flow 215228
- Analogies between Riemann problem for 1-D fluid dynamics and 2-D steady supersonic flow 225238
- Instability and ill-posedness in granular flow 241254
- Well-posedness of the Riemann problem; consistency of the Godunov's scheme 251264
- The Riemann problem for a system of conservation laws modeling phase transitions 267280
- Detonation waves and deflagration waves in the one dimensional ZND model for high Mach number combustion 277290
- The Riemann solution to a system of conservation laws, with application to a non-zero sum game 287300
- Asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in several dimensions 299312
- Riemann problem for a combustion model system: the existence and basic structure of the self-similar solutions 305318
- Dynamic instability of the liquid crystal director 325338
- On the Riemann problem for a prototype of a mixed type conservation law. II 331344