Contemporary Mathematics 1989; 367 pp; softcover Volume: 100 ISBN10: 0821851063 ISBN13: 9780821851067 List Price: US$60 Member Price: US$48 Order Code: CONM/100
 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 theorythat 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), viscoelastic materials, phase transitions, and multiphase flow in porous media. In addition to their usefulness in largescale calculations, computational schemes have vastly improved the handling of discontinuity behavior. This volume contains the proceedings of the AMSIMSSIAM 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  D. Hoff and T.P. Liu  Shock wave solutions of the \(1d\) NavierStokes equations for compressible isentropic flow
 G. Schleiniger, M. C. Calderer, and L. P. Cook  Embedded hyperbolic regions in a nonlinear model for viscoelastic flow
 I. Aavatsmark  Capillary energy and the entropy condition for the BuckleyLeverett equation
 S. S. Antman and W. G. Szymczak  Nonlinear elastoplastic waves
 M. Brio  An example of a Riemann problem of second kind
 B. G. Bukiet  Density profiles for diverging detonations
 J. Grove  Anomalous waves in shock wavefluid interface collisions
 D. S. Malkus, J. Nohel, and B. Plohr  Timedependent shear flow of a nonNewtonian fluid
 T. Zhang  The Riemann problem for combustion
 E. Isaacson, D. Marchesin, and B. Plohr  Transitional shock waves
 J. Trangenstein  Threephase flow with gravity
 B. Bohannon  A system of conservation laws with a parabolic degeneracy
 J. Hunter  Nonlinear surface waves
 B. L. Keyfitz  A criterion for certain wave structures in systems that change type
 D. Marchesin and H. B. Medeiros  A note on the stability of eigenvalue degeneracy in nonlinear conservation laws of multiphase flow
 R. Menikoff  Analogies between Riemann problem for \(1D\) fluid dynamics and \(2D\) steady supersonic flow
 E. B. Pitman and D. G. Schaeffer  Instability and illposedness in granular flow
 H. Gilquin and D. Serre  Wellposedness of the Riemann problem; consistency of the Godunov's scheme
 V. Roytburd  The Riemann problem for a system of conservation laws modeling phase transitions
 D. Wagner  Detonation waves and deflagration waves in the one dimensional ZND model for high Mach number combustion
 G.Q. Chen and A. Rustichini  The Riemann solution to a system of conservation laws, with application to a nonzero sum game
 Z. Xin  Asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in several dimensions
 E.Z. Fu, T. Tao, and Z.H. Teng  Riemann problem for a combustion model system: the existence and basic structure of the selfsimilar solutions
 R. Saxton  Dynamic instability of the liquid crystal director
 H. Holden and L. Holden  On the Riemann problem for a prototype of a mixed type conservation law. II
