A Kinetic Equation with Kinetic Entropy Functions for Scalar Conservation Laws
Author: Institute for Computer Applications in Science and Engineering
Publisher:
Published: 1990
Total Pages: 28
ISBN-13:
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Author: Institute for Computer Applications in Science and Engineering
Publisher:
Published: 1990
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKAuthor: B. Perthame
Publisher: Oxford University Press
Published: 2002-12-05
Total Pages: 212
ISBN-13: 9780198509134
DOWNLOAD EBOOKWritten 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).
Author: Seok Hwang
Publisher:
Published: 2002
Total Pages: 76
ISBN-13:
DOWNLOAD EBOOKAuthor: Alexander Sinitsyn
Publisher: Elsevier
Published: 2011-06-17
Total Pages: 321
ISBN-13: 0123877806
DOWNLOAD EBOOKBoltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions
Author: Constantine M. Dafermos
Publisher: Springer
Published: 2016-05-26
Total Pages: 852
ISBN-13: 3662494515
DOWNLOAD EBOOKOLD TEXT 4th Edition to be replaced: This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews
Author: Niva B Maslova
Publisher: World Scientific
Published: 1993-03-10
Total Pages: 216
ISBN-13: 9814505161
DOWNLOAD EBOOKThe 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.
Author:
Publisher:
Published: 1990
Total Pages: 252
ISBN-13:
DOWNLOAD EBOOKAuthor: C. M. Dafermos
Publisher: 清华大学出版社有限公司
Published: 2005
Total Pages: 466
ISBN-13: 9787302102038
DOWNLOAD EBOOKAuthor: Sylvie Benzoni-Gavage
Publisher: Springer Science & Business Media
Published: 2008-01-12
Total Pages: 1117
ISBN-13: 3540757120
DOWNLOAD EBOOKThis 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.
Author: Shi Jin
Publisher: Springer
Published: 2018-03-20
Total Pages: 282
ISBN-13: 3319671103
DOWNLOAD EBOOKThis 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.