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Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed.
This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems.
Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, 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 of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.
Volume.- Convergence of a Staggered Lax-Friedrichs Scheme on Unstructured 2D-grids.- Viscous and Relaxation Approximations to Heteroclinic Traveling Waves of Conservation Laws with Source Terms.- Adaptive FE Methods for Conservation Equations.- The Entropy Rate Admissibility Criterion for a Phase Transition Problem.- Dust Formation in Turbulent Media.- Existence of a Weak Solution for a Quasilinear Wave Equation with Boundary Condition.- Asymptotic Behavior of Entropy Weak Solution for Hyperbolic System with Damping.- On the Existence of Semidiscrete Shock Profiles.- On the Convergence Rate of Operator Splitting for Weakly Coupled Systems of Hamilton-Jacobi Equations.- Composite Schemes on Triangular Meshes.- Asymptotic-Preserving (AP) Schemes for Multiscale Kinetic Equations:A Unified Approach.- A Kinetic Approach to Hyperbolic Systems and the Role of Higher Order Entropies.- Stationary Waves for the Discrete Boltzmann Equations in the Half Space.- Divergence Corrections in the Numerical Simulation of Electromagnetic Wave Propagation.- Numerical Investigation of Examples of Unstable Viscous Shock Waves...- Proving Existence of Nonlinear Differential Equations Using Numerical Approximations.- Asymptotic Behavior of Hyperbolic Boundary Value Problems with Relaxation Term.- A Wave Propagation Algorithm for the Solution of PDEs on the Surface of a Sphere.- On the L1Stability of Multi-shock Solutions to the Riemann Problem….- Stable, Oscillatory Viscous Profiles of Weak Shocks in Systems of Stiff Balance Laws.- Shallow Water Conservation Laws on a Sphere.- Riemann Solutions for a Model of Combustion in Two-Phase Flow in Porous Media.- Theory of Three-Phase Flow Applied to Water-Alternating-Gas Enhanced Oil Recovery.- Preconditioned Krylov Subspace Methods for Hyperbolic Conservation Laws.- The Riemann Problem for Nonlinear Elasticity.- ADER: Arbitrary-Order Non-Oscillatory Advection Schemes.- Extended Thermodynamics — the Physics and Mathematics of the Hyperbolic Equations of Thermodynamics.- Enforcing Gauss’ Law in Computational Electromagnetics within a Finite-volume Framework.- Discrete BGK Models for Dynamic Phase Transitions in One-Dimension..- An Adaptive Staggered Grid Scheme for Conservation Laws.- Solutions to Scalar Conservation Laws Where the Flux is Discontinuous in Space and Time.- Overcompressive Shocks and Compound Shocks in 2D and 3D Magnetohydrodynamic Flows.- Aspects of a Numerical Procedure for Two-Phase Flow Models.- On a Nonexistence of Global Smooth Solutions to Compressible Euler Equations.- Central Schemes for Balance Laws.- Estimates for Pseudo-differential and Hyperbolic Differential Equations via Fourier Integrals with Complex Phases.- Existence of Travelling Fronts for Nonlinear Transport Equations.- Nonlinear Wave Propagation in Close to Hyperbolic Systems.- Shock-Wave Cosmology.- On a Second Order Residual Estimator for Nonlinear Conservation Laws..- Error Estimates of Approximate Solutions for Nonlinear Scalar Conservation Laws.- Solution of the Boltzmann Equation in Stiff Regime.- Characteristics and Riemann Invariants of the Kinetic Integrodifferential Equations of Bubbly Flow.- A LSQ-SPH Approach for Solving Compressible Viscous Flows.- On Stability of Fast Shock Waves in Classical and Relativistic MHD.- Remarks on Hyperbolic Relaxation Systems.- Wave Interactions in Nonlinear Strings.- List of Participants.- Author Index.