eBook ISBN:  9780821876886 
Product Code:  CONM/100.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876886 
Product Code:  CONM/100.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 100; 1989; 367 ppMSC: Primary 00; Secondary 35; 65; 76
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), 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

Articles

David Hoff and TaiPing Liu — Shock wave solutions of the $1$d NavierStokes equations for compressible, isentropic flow [ MR 1033504 ]

G. Schleiniger, M. C. Calderer and L. Pamela Cook — Embedded hyperbolic regions in a nonlinear model for viscoelastic flow [ MR 1033505 ]

Ivar Aavatsmark — Capillary energy and the entropy condition for the BuckleyLeverett equation [ MR 1033506 ]

Stuart S. Antman and William G. Szymczak — Nonlinear elastoplastic waves [ MR 1033507 ]

M. Brio — An example of a Riemann problem of second kind [ MR 1033508 ]

Bruce G. Bukiet — Density profiles for diverging detonations [ MR 1033509 ]

John W. Grove — Anomalous waves in shock wave—Fluid interface collisions

David S. Malkus, John A. Nohel and Bradley J. Plohr — Timedependent shear flow of a nonNewtonian fluid

Tong Zhang — The Riemann problem for combustion [ MR 1033512 ]

Eli L. Isaacson, Dan Marchesin and Bradley J. Plohr — Transitional shock waves [ MR 1033513 ]

John A. Trangenstein — Threephase flow with gravity [ MR 1033514 ]

Barbara Bohannon — A system of conservation laws with a parabolic degeneracy [ MR 1033515 ]

John K. Hunter — Nonlinear surface waves [ MR 1033516 ]

Barbara Lee Keyfitz — A criterion for certain wave structures in systems that change type [ MR 1033517 ]

Dan Marchesin and Heloisa B. Medeiros — A note on the stability of eigenvalue degeneracy in nonlinear conservation laws of multiphase flow [ MR 1033518 ]

Ralph Menikoff — Analogies between Riemann problem for $1$D fluid dynamics and $2$D steady supersonic flow [ MR 1033519 ]

E. Bruce Pitman and David G. Schaeffer — Instability and illposedness in granular flow [ MR 1033520 ]

H. Gilquin and D. Serre — Wellposedness of the Riemann problem; consistency of the Godunov’s scheme [ MR 1033521 ]

Victor Roytburd — The Riemann problem for a system of conservation laws modeling phase transitions [ MR 1033522 ]

David H. Wagner — Detonation waves and deflagration waves in the onedimensional ZND model for high Mach number combustion [ MR 1033523 ]

Gui Qiang Chen and Aldo Rustichini — The Riemann solution to a system of conservation laws, with application to a nonzero sum game [ MR 1033524 ]

Zhou Ping Xin — Asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in several dimensions [ MR 1033525 ]

En Zhong Fu, Tao Tang and Zhen Huan Teng — Riemann problem for a combustion model system: the existence and basic structure of the selfsimilar solutions [ MR 1033526 ]

R. A. Saxton — Dynamic instability of the liquid crystal director [ MR 1033527 ]

Helge Holden and Lars Holden — On the Riemann problem for a prototype of a mixed type conservation law. II [ MR 1033528 ]


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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), 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.

Articles

David Hoff and TaiPing Liu — Shock wave solutions of the $1$d NavierStokes equations for compressible, isentropic flow [ MR 1033504 ]

G. Schleiniger, M. C. Calderer and L. Pamela Cook — Embedded hyperbolic regions in a nonlinear model for viscoelastic flow [ MR 1033505 ]

Ivar Aavatsmark — Capillary energy and the entropy condition for the BuckleyLeverett equation [ MR 1033506 ]

Stuart S. Antman and William G. Szymczak — Nonlinear elastoplastic waves [ MR 1033507 ]

M. Brio — An example of a Riemann problem of second kind [ MR 1033508 ]

Bruce G. Bukiet — Density profiles for diverging detonations [ MR 1033509 ]

John W. Grove — Anomalous waves in shock wave—Fluid interface collisions

David S. Malkus, John A. Nohel and Bradley J. Plohr — Timedependent shear flow of a nonNewtonian fluid

Tong Zhang — The Riemann problem for combustion [ MR 1033512 ]

Eli L. Isaacson, Dan Marchesin and Bradley J. Plohr — Transitional shock waves [ MR 1033513 ]

John A. Trangenstein — Threephase flow with gravity [ MR 1033514 ]

Barbara Bohannon — A system of conservation laws with a parabolic degeneracy [ MR 1033515 ]

John K. Hunter — Nonlinear surface waves [ MR 1033516 ]

Barbara Lee Keyfitz — A criterion for certain wave structures in systems that change type [ MR 1033517 ]

Dan Marchesin and Heloisa B. Medeiros — A note on the stability of eigenvalue degeneracy in nonlinear conservation laws of multiphase flow [ MR 1033518 ]

Ralph Menikoff — Analogies between Riemann problem for $1$D fluid dynamics and $2$D steady supersonic flow [ MR 1033519 ]

E. Bruce Pitman and David G. Schaeffer — Instability and illposedness in granular flow [ MR 1033520 ]

H. Gilquin and D. Serre — Wellposedness of the Riemann problem; consistency of the Godunov’s scheme [ MR 1033521 ]

Victor Roytburd — The Riemann problem for a system of conservation laws modeling phase transitions [ MR 1033522 ]

David H. Wagner — Detonation waves and deflagration waves in the onedimensional ZND model for high Mach number combustion [ MR 1033523 ]

Gui Qiang Chen and Aldo Rustichini — The Riemann solution to a system of conservation laws, with application to a nonzero sum game [ MR 1033524 ]

Zhou Ping Xin — Asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in several dimensions [ MR 1033525 ]

En Zhong Fu, Tao Tang and Zhen Huan Teng — Riemann problem for a combustion model system: the existence and basic structure of the selfsimilar solutions [ MR 1033526 ]

R. A. Saxton — Dynamic instability of the liquid crystal director [ MR 1033527 ]

Helge Holden and Lars Holden — On the Riemann problem for a prototype of a mixed type conservation law. II [ MR 1033528 ]