Hyperbolic Problems: Theory, Numerics, Applications

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 made considerable progress and 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 on hyperbolic problems. Applications covered include: one-phase and multiphase fluid flow; phase transitions; shallow-water dynamics; elasticity; extended thermodynamics; electromagnetism; classical and relativistic magnetohydrodynamics; and 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, and travelling fronts for transport equations. Numerically oriented articles study finite difference, finite volume and finite element schemes, adaptive, multiresolution and artificial dissipation methods. The book is intended for researchers and graduate students in mathematics, science and engineering.