Kinetic Formulation of Conservation Laws

Kinetic Formulation of Conservation Laws
Author: B. Perthame
Publisher: Oxford University Press
Total Pages: 212
Release: 2002-12-05
Genre: Language Arts & Disciplines
ISBN: 9780198509134

Written by a well-known expert in the field, the focus of this book is on an innovative mathematical and numerical theory which applies to classical models of physics such as shock waves and balance laws. The text is based on early works in common with P.L. Lions (field medalist).

Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics
Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
Total Pages: 710
Release: 2009-12-12
Genre: Mathematics
ISBN: 3642040489

The 3rd edition is thoroughly revised, applications are substantially enriched, it includes a new account of the early history of the subject (from 1800 to 1957) and a new chapter recounting the recent solution of open problems of long standing in classical aerodynamics. The bibliography comprises now over fifteen hundred titles. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH

Nonlinear Evolution Equations: Kinetic Approach

Nonlinear Evolution Equations: Kinetic Approach
Author: Niva B Maslova
Publisher: World Scientific
Total Pages: 216
Release: 1993-03-10
Genre: Mathematics
ISBN: 9814505161

The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.

Hyperbolic Problems: Theory, Numerics, Applications

Hyperbolic Problems: Theory, Numerics, Applications
Author: Sylvie Benzoni-Gavage
Publisher: Springer Science & Business Media
Total Pages: 1117
Release: 2008-01-12
Genre: Mathematics
ISBN: 3540757120

This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.

Uncertainty Quantification for Hyperbolic and Kinetic Equations

Uncertainty Quantification for Hyperbolic and Kinetic Equations
Author: Shi Jin
Publisher: Springer
Total Pages: 282
Release: 2018-03-20
Genre: Mathematics
ISBN: 3319671103

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Hyperbolic Problems: Theory, Numerics, Applications

Hyperbolic Problems: Theory, Numerics, Applications
Author: Heinrich Freistühler
Publisher: Birkhäuser
Total Pages: 471
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034883722

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.