Current Progress in Hyperbolic Systems: Riemann Problems and Computations: Proceedings of the AMS-IMS-SIAM Joint Summer Conference Held July 16-22, 1988 with Support from the National Science Foundation and the Office of Naval Research

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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.
 

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Contents

Shock wave solutions of the 1d NavierStokes equations for compressible isentropic flow
1
Embedded hyperbolic regions in a nonlinear model for viscoelastic flow
9
Capillary energy and the entropy condition for the BuckleyLeverett equation
21
Nonlinear elastoplastic waves
27
An example of a Riemann problem of second kind
55
Density profiles for diverging detonations
63
Anomalous waves in shock wave fluid interface collisions
77
Timedependent shear flow of a nonNewtonian fluid
91
A criterion for certain wave structures in systems that change type
203
A note on the stability of eigenvalue degeneracy in nonlinear conservation laws of multiphase flow
215
Analogies between Riemann problem for 1D fluid dynamics and 2D steady supersonic flow
225
Instability and illposedness in granular flow
241
Wellposedness of the Riemann problem consistency of the Godunovs scheme
251
The Riemann problem for a system of conservation laws modeling phase transitions
267
Detonation waves and deflagration waves in the one dimensional ZND model for high Mach number combustion
277
The Riemann solution to a system of conservation laws with application to a nonzero sum game
287

The Riemann problem for combustion
111
Transitional shock waves
125
Threephase flow with gravity
147
A system of conservation laws with a parabolic degeneracy
161
Nonlinear surface waves
185
Asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in several dimensions
299
the existence and basic structure of the selfsimilar solutions
305
Dynamic instability of the liquid crystal director
325
On the Riemann problem for a prototype of a mixed type conservation law II
331
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