Heinrich Freistühler – författare

This volume provides a comprehensive treatment of central themes in the modern mathematical theory of shock waves. Authored by leading scientists in the area, the five unified articles cover: * the Cauchy problem for hyperbolic systems of conservation laws (T.-P.Liu) * the stability problem for shock waves in the hyperbolic (inviscid) setting (G. Metivier) * shock wave solutions of the Einstein-Euler equations of General Relativity (J. Smoller and B. Temple) * fundamental properties of hyperbolic systems with relaxation (W.-A. Yong) * the stability problem for shock waves in the parabolic (viscous) setting (K. Zumbrun) Recent Advances in the Theory of Shock Waves combines the rigor of mathematical analysis with attention to the physical origins of the field. The topics covered provide ideal starting points for seminars and courses for mathematicians, physicists, and theoretically motivated engineers.

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein­ Euler equations of general relativity; indeed, the mathematical and physical con­ sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap­ proach had for a long time seemed out of reach. The stability problem for "in­ viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi­ group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop­ erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

This volume presents seven invited lecture series from the DFG Priority Programme Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness, surveying recent developments in mathematical fluid dynamics across a broad range of scales, from kinetic theory to turbulence, mixing, and relativistic flows. The contributions reflect current research directions in the field. Hana Mizerová and Simon Markfelder discuss aspects of the emerging theory of non-standard weak and generalized solutions to the compressible Euler equations. Theodore Drivas addresses turbulence, Gianluca Crippa studies mixing phenomena, Tai‑Ping Liu and Shih‑Hsien Yu develop the theory of nonlinear waves for the Boltzmann equation, and Marcelo Disconzi focuses on dissipative relativistic fluid dynamics.The volume is intended for researchers and advanced graduate students in partial differential equations and applied mathematics.

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.

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.

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 volume is part of a two-volume set of conference proceedings which 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.

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 volume is part of a two-volume set of conference proceedings containing 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.