Nonlinear Hyperbolic Problems: Proceedings of an Advanced Research Workshop held in St. Etienne, France January 13–17, 1986

A. Bourgeade, P. Le Floch, P. A. Raviart (auth.), Claude Carasso, Denis Serre, Pierre-Arnaud Raviart (eds.)9780387182001, 0-387-18200-4

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 application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

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Table of contents :
Approximate solution of the generalized Riemann problem and applications….Pages 1-9
Computation of oscillatory solutions to partial differential equations….Pages 10-22
Preliminary results on the extension of eno schemes to two-dimensional problems….Pages 23-40
Upwind differencing schemes for hyperbolic conservation laws with source terms….Pages 41-51
The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes….Pages 52-63
2-D and 3-D Euler computations with finite element methods in aerodynamics….Pages 64-81
A “box-scheme” for the euler equations….Pages 82-102
Numerical techniques in elastoplasticity….Pages 103-114
An implicit centered scheme which gives non-oscillatory steady shocks….Pages 115-127
A computer-aided system for investigation and construction of difference schemes of gas dynamics….Pages 128-134
Lois de conservation et integrales d’energie des equations hyperboliques….Pages 135-149
On symmetrizing hyperbolic differential equations….Pages 150-151
A survey of nonstrictly hyperbolic conservation laws….Pages 152-162
Admissibility criteria for phase boundaries….Pages 163-171
The transformation from Eulerian to Lagrangian coordinates for solutions with discontinuities….Pages 172-180
Two existence theorems for systems of conservation laws with dissipation….Pages 181-194
Global solutions to some free boundary problems for quasilinear hyperbolic systems and applications….Pages 195-209
Un theoreme d’existence globale en elasticite non lineaire mono-dimensionnelle….Pages 210-220
A nonhomogeneous system of equations of nonisentropic gas dynamics….Pages 221-237
Far field boundary conditions for steady state solutions to hyperbolic systems….Pages 238-252
Can hyperbolic systems of conservation laws be well-posed in BV(R;R N )?….Pages 253-264
Propagation des oscillations dans les systemes hyperboliques non lineaires….Pages 265-285
Stability and decay in systems of conservation laws….Pages 286-307
Different approach for the relation between the kinetic and the macroscopic equations….Pages 308-323
Integrable transport processes….Pages 324-341