Nonlinear Hyperbolic Problems Proceedings of an Advanced Research Wo
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in applicatio
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1270 C. Carasso P-A. Raviart D. Serre (Eds.)
Nonlinear Hyperbolic Problems Proceedings of an Advanced Research Workshop held in St. Etienne, France January 13-17, 1986
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Claude Carasso Denis Serre Analyse Numerique, 23 rue du Dr. Paul Michelon 42023 Saint Etienne Cedex 2, France Pierre-Arnaud Raviart Universite Pierre et Marie Curie Analyse Nurnerique 4, place Jussieu 75230 Paris Cedex 05, France
Mathematics Subject Classification (1980): 35L, 65M, 76N
ISBN 3-540-18200-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18200-4 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broedcastinqreproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
CONTENTS I Numerical Analysis
a - General theory.
A.Bourgeade, Ph.Le Floch, P.A.Raviart: Approximate solution of the generalized Riemann problem and applications. B.Engquist: Computation of oscillatory solutions to partial differential equations. A.Harten: Preliminary results on the extension of ENO schemes to two-dimensional problems. P.L.Roe: Upwind differencing schemes for hyperbolic conservation laws with source terms. E.Tadmor: The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes. b Main applications. V.Billey, J.Periaux, P.Perrier, B.Stoumet: 2-D and 3-D Euler computations with [mite element methods in aerodynamics. J-J.Chattot, S.Malet: A "box-scheme" for the Euler equations. J-F.Colombeau, A-Y.Leroux: Numerical techniques in elastoplasticity. V.Daru, A.Lerat: An implicit centered scheme which gives non-oscillatory steady shocks. y. I.Shokin: A computer aided system for investigation and construction of difference schemes of gas dynamics. II fuperbolic
eD E
10 23 41 52
64
82 103 115
128
theory
a - Surveys, open questions.
S.K.Godunov: Lois de conservation et integrales d'energie des equations hyperboliques. P.D.Lax: On symmetrizing hyperbolic differential equations. B-L.Keyfitz: A sUIVey of nonstrictly hyperbolic conservation laws.
135
150 152
163 M.Slemrod: Admissibility criteria for phase boundaries. D.H.Wagner: The transformation from Eulerian to Lagrangian coordinates for solutions with discontinuities. 172 b Existence theory.
D.Hoff: Two existence theorems for systems of conservation laws with dissipation.
181
IV
Li Ta Tsien: Global solutions for some free boundary value problems for quasilinear hyperbolic s
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