Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics PDF

Author: Constantine M. Dafermos

Publisher: Springer Science & Business Media

Published: 2009-12-12

Total Pages: 710

ISBN-13: 3642040489

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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

Hyperbolic Conservation Laws in Continuum Physics

Hyperbolic Conservation Laws in Continuum Physics PDF

Author: Constantine M. Dafermos

Publisher: Springer Science & Business Media

Published: 2006-01-16

Total Pages: 636

ISBN-13: 3540290893

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This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. 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

Hyperbolic Systems of Conservation Laws

Hyperbolic Systems of Conservation Laws PDF

Author: Philippe G. LeFloch

Publisher: Springer Science & Business Media

Published: 2002-07-01

Total Pages: 1010

ISBN-13: 9783764366872

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This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

Elements of Continuum Mechanics and Conservation Laws

Elements of Continuum Mechanics and Conservation Laws PDF

Author: S.K. Godunov

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 263

ISBN-13: 1475751176

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Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

Hyperbolic Conservation Laws and the Compensated Compactness Method

Hyperbolic Conservation Laws and the Compensated Compactness Method PDF

Author: Yunguang Lu

Publisher: CRC Press

Published: 2002-09-27

Total Pages: 254

ISBN-13: 1420035576

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The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Comp

Hyperbolic Systems of Balance Laws

Hyperbolic Systems of Balance Laws PDF

Author: Alberto Bressan

Publisher: C.I.M.E. Foundation Subseries

Published: 2007-06-06

Total Pages: 372

ISBN-13:

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The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case.

One-dimensional Hyperbolic Conservation Laws And Their Applications

One-dimensional Hyperbolic Conservation Laws And Their Applications PDF

Author: Jean-michel Coron

Publisher: World Scientific

Published: 2019-01-08

Total Pages: 395

ISBN-13: 9813276193

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This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

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