Hyperbolic Problems: Theory, Numerics, Applications

The Eighth International Conference on Hyperbolic Problems - Theory, Nu­ merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con­ tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug­ gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computation is of fundamental importance. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther­ modynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability ofshock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite ele­ ment schemes, adaptive, multiresolution, and artificial dissipation methods.

Ghost-Fluids for the Poor: A Single Fluid Algorithm for Multifluids.- Propagation of Smoothness for Edge-degenerate Wave Equations.- Front Tracking for Non Genuinely Nonlinear Conservation Laws.- Well-Posedness for Non Genuinely Nonlinear Conservation Laws.- Wave Phenomena at Liquid-solid Interfaces.- Diffusive Discrete BGK Schemes for Nonlinear Hyperbolic-parabolic Systems.- Non-oscillatory Lax-Friedrichs type Central Finite Volume Methods for 3-D Flows on Unstructured Tetrahedral Grids.- Stability of Maxwell States in Thermo-Elasticity.- The Riemann-Problem in Extended Thermodynamics.- Heterogeneous Domain Decomposition Methods for Compressible Magneto-plasma Flows.- Magnetoplasmadynamic Rocket Thruster Simulation.- The Eikonal Equation on a Manifold. Applications to Grid Generation or Refinement.- Crossflow Instabilities in the Approximation of Detonation Waves.- Wave Propagation Algorithms for Hyperbolic Systems on Curved Manifolds.- The Random Projection Method for Stiff Multi-species Detonation Computation.- On the Stability of Large Amplitude Semi-discrete Shock Profiles by Means of an Evans Function in Infinite Dimensions.- Viscosity Solutions for Hyperbolic Systems where Shock Curves are Straight Lines.- Adaptive Finite Elements for Stationary Compressible Flows at Low Mach Number.- A Monge-Kantorovich Approach to the Maxwell Equations.- Convergence of the Godunov Scheme for Straight Line Systems.- The Convergence of Multicomponent Chromatography with Relaxation.- A Strongly Degenerate Convection-diffusion Problem Modeling Centrifugation of Flocculated Suspensions.- Weak Shock Reflection Modeled by the Unsteady Transonic Small Disturbance Equation.- A Hyperbolic System of Conservation Laws in Modeling Endovascular Treatment of Abdominal Aortic Aneurysm.- Study on Supersonic Flow Past a Pointed Body.- Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme.- Multiresolution Analysis on Triangles: Application to Gas Dynamics.- Propagation and Interaction of Nonlinear Waves to Quasilinear Equations.- MHD Instabilities Arising in Solar Physics: A Numerical Approach.- Numerical Methods for the Real Gas MHD Equations.- Towards a Kinetic Model of Thrbulent Incompressible Fluids.- Parabolic Relaxation of Semilinear Multidimensional Hyperbolic Systems.- Large Time Asymptotics in Contaminant Transport in Porous Media with Variable Diffusion.- A Nonlinear Flux Vector Split Defect Correction Scheme for Fast Solutions of the Euler and Navier-Stokes Equations.- A Continuous Dependence Result for Nonlinear Degenerate Parabolic Equations with Spatially Dependent Flux Function.- A Lagrangian Central Scheme for Multi-Fluid Flows.- Ultimate Boundedness, Propagation of Oscillations, and the Long-time Behaviour of Solutions to the Navier-Stokes Equations of Compressible Fluid Flows.- Adaptive Methods for the Solution of Compressible Flow.- The MoT-ICE: A New Multi-dimensional Wave-propagation-algorithm Based on Fey’s Method of Transport. With Application to the Eulerand MHD-equations.- Posit ive Decompositions of the Euler Equations into Advection Equations.- The Einstein-Dirac-Yang/Mills Equations: Black Holes.- A Numerical Study on Viscous Profiles of MHD Shock Waves.- A Vanishing Debye Length Limit in a Hydrodynamic Model for Semiconductors.- Dynamic Mesh Adapt ion for Supersonic Reactive Flow.- A High-Resolution Scheme for the Elastic-Plastic Wave Equation.- Stability for Temple Class Systems with L?Boundary Data.- Linear Stability of Shock Profiles for Systems of Conservation Laws with Semi-linear Relaxation.- A Nonconservative Numerical Approach for Hyperbolic Systems with Source Terms: The Well-Balanced Schemes.- Multidimensional Artificial Dissipation for t he Numerical Approximation of Conservation Laws.- Author Index.