Hyperbolic Problems: Theory, Numerics, Applications

InfotextThese are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Inhalt
A New Approach for a Flux Solver Taking into Account Source Terms, Viscous and Multidimensional Effects.- Blowup for Hyperbolic Equations.- Some Analytical Results Concerning the Drift Diffusion Equations for Semiconductor Devices Coupled with Maxwell's Equations.- Transport Equations and Orlicz Spaces.- Well-posedness of a 2 x 2 System of Resonant Conservation Laws.- The Relaxation Limit for Systems of Broadwell Type.- Weakly-nonlinear Hyperbolic Waves in BZT-fluids.- Inclusion of Solutions of Cauchy Problems for Quasilinear Hyperbolic Equations.- A Fed Back Level-Set Method for Moving Material-Void Interfaces.- Mathematical Aspects of Numerical Solution of Hyperbolic Systems.- Existence of Entropy Solutions for the Compressible Euler Equations.- Wave Propagation Methods for Conservation Laws with Source Terms.- Quasi-Characteristics Numerical Schemes.- On the Initial-value Problem for Zero-pressure Gas Dynamics.- Stability and Instability of Detonation Waves.- Central Schemes for Systems of Balance Laws.- Composite Centered Schemes for Multidimensional Conservation Laws.- On the Diffusion Limit of a Hyperbolic Relaxation System.- Well-Posedness Theory for System of Hyperbolic Conservation Laws.- Nonlinear Stability of Shock Fronts for a Relaxation System in Several Space Dimensions.- Front Tracking Based on Conservation in One and Two Space Dimensions.- A Genuinely Multi-dimensional Scheme for Mixed Hyperbolic-Parabolic Systems.- Recent Results in Non Linear Geometric Optics.- Evolution-Galerkin Methods: Algorithms and Analysis from a Finite Difference Viewpoint.- Hyperbolic Relaxation Approximation to Nonlinear Parabolic Problems.- A Comparison of Third and Second Order Accurate Finite Volume Schemes for the Two-dimensional Compressible Euler Equations.- UniqueSolutions to Discontinuous Hamilton-Jacobi Equations in Shape-From-Shading.- Relativistic Dissipative Hydrodynamics in the 3+1 Formulation.- Absolutely Transparent Boundary Conditions for Time-Dependent Wave-Type Problems.- Blow-up of Solutions in System of Atmosphere Dynamics.- Holomorphic Factorization for the Solution Operators for Hyperbolic Equations.- The Propagation of Shock Waves in 2-D System of Pressureless Gas Dynamics.- Hyperbolic Systems with Relaxation: Symmetrizers and Entropies.- Some Hyperbolic Models for Wave Propagation.- Discrete Shock Profiles and Their Stability.- Advances in Fast Marching and Level Set Methods for Propagating Interfaces.- Rate of Convergence for the Zero Relaxation Limit.- A High Order Fourier/Unstructured Discontinuous Galerkin Method for Hyperbolic Conservation Laws.- Asymptotic Properties of Solutions to High-Order Hyperbolic Equations Generalizing the Damped Wave Equation.- A Volume-of-fluid Type Algorithm for Compressible Two-phase Flows.- Numerical Code for Magneto-Plasma Flows.- Highly-Accurate Artificial Boundary Conditions for Unsteady Transonic Flow Problems in Wind Tunnels.- Pointwise Convergence Rate for Nonlinear Conservation Laws.- Newton-GMRES Resolution of Ill Conditioned Hyperbolic Systems in Fluid Dynamics.- Applications of Shock-Waves in General Relativity.- The Riemann Problem for the Integrodifferential Equations of the Shallow Water Theory.- Decay and Uniqueness of Solutions of Nonlinear Hyperbolic Conservation Laws via Generalized Characteristics.- Radiative Shocks, Supersonic Turbulence and Structure Formation in Space.- A New Convergence Proof for FV Schemes.- The Particle Model of Compressible Fluids.- The Method of Transport for the Euler Equations Written as a Kinetic Scheme.- List of Participants.