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© 2010

Hyperbolic Conservation Laws in Continuum Physics

  • The author is unquestionably the greatest authority on the subject as well as a masterly writer

  • The 3rd edition is thoroughly revised, up-to-date and includes new material on the early history of the subject, and a new chapter recounting recent solution of open problems of long standing in classical aerodynamics

  • The expanded bibliography comprises now over fifteen hundred titles

Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 325)

Table of contents

  1. Front Matter
    Pages i-xxxv
  2. Constantine M. Dafermos
    Pages 1-24
  3. Constantine M. Dafermos
    Pages 25-51
  4. Constantine M. Dafermos
    Pages 53-74
  5. Constantine M. Dafermos
    Pages 75-96
  6. Constantine M. Dafermos
    Pages 97-144
  7. Constantine M. Dafermos
    Pages 145-194
  8. Constantine M. Dafermos
    Pages 195-229
  9. Constantine M. Dafermos
    Pages 231-269
  10. Constantine M. Dafermos
    Pages 271-324
  11. Constantine M. Dafermos
    Pages 325-330
  12. Constantine M. Dafermos
    Pages 331-372
  13. Constantine M. Dafermos
    Pages 373-433
  14. Constantine M. Dafermos
    Pages 435-475
  15. Constantine M. Dafermos
    Pages 477-515
  16. Constantine M. Dafermos
    Pages 545-571
  17. Constantine M. Dafermos
    Pages 573-596
  18. Back Matter
    Pages 597-708

About this book

Introduction

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.

New to the 3rd edition is an account of the early history of the subject, spanning the period between 1800 to 1957. Also new is a chapter recounting the recent solution of open problems of long standing in classical aerodynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised and brought up to date, and the collection of applications has been substantially enriched. The bibliography, also expanded and updated, now comprises over fifteen hundred titles.

From the reviews of the 2nd edition:

"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." Evgeniy Panov, Zentralblatt MATH

"This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful." Katarina Jegdic, SIAM Review

Keywords

aerodynamics conservation laws continuum mechanics hyperbolic systems mechanics partial differential equations shock waves stability thermodynamics

Authors and affiliations

  1. 1.Div. Applied MathematicsBrown UniversityProvidenceU.S.A.

About the authors

Professor Dafermos received a Diploma in Civil Engineering from the National Technical University of Athens (1964) and a Ph.D. in Mechanics from the Johns Hopkins University (1967). He has served as Assistant Professor at Cornell University (1968-1971),and as Associate Professor (1971-1975) and Professor (1975- present) in the Division of Applied Mathematics at Brown University. In addition, Professor Dafermos has served as Director of the Lefschetz Center of Dynamical Systems (1988-1993, 2006-2007), as Chairman of the Society for Natural Philosophy (1977-1978) and as Secretary of the International Society for the Interaction of Mathematics and Mechanics. Since 1984, he has been the Alumni-Alumnae University Professor at Brown.

In addition to several honorary degrees, he has received the SIAM W.T. and Idalia Reid Prize (2000), the Cataldo e Angiola Agostinelli Prize of the Accademia Nazionale dei Lincei (2011), the Galileo Medal of the City of Padua (2012), and the Prize of the International Society for the Interaction of Mechanics and Mathematics (2014). He was elected a Fellow of SIAM (2009) and a Fellow of the AMS (2013). In 2016 he received the Wiener Prize, awarded jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).

Bibliographic information

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Reviews

From the reviews of the second edition:

"The second edition of the famous book Grundlehren der Mathematischen Wissenschaften 325 is devoted to the mathematical theory of hyperbolic conservation and balance laws. 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. … the original text has been reorganized so as to streamline the exposition, enrich the collection of examples, and improve the notation. … The bibliography has been considerably expanded … ." (Evgeniy Panov, Zentralblatt MATH, Vol. 1078, 2006)

"This comprehensive book is about rigorous mathematical theory of balance and conservation laws … . The statements of theorems are carefully and precisely written. The proofs are canonical and illuminating … . This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful. I heartily recommend this book to anyone who wants to learn about the foundations of the theory of balance and conservation laws and their generic relations to continuum physics … ." (Katarina Jegdic, SIAM Review, Vol. 48 (3), 2006)

From the reviews of the third edition:

“Covers the existence, uniqueness, continuous dependence, and qualitative behavior of entropy solutions for, successively, scalar conservation laws, systems of two conservation laws, and general strictly hyperbolic systems. … This book is now widely recognized as the ‘Bible’ on hyperbolic conservation laws, and has contributed to the training of many students while providing a huge amount of invaluable information (including a 100 page bibliography) for researchers working in this field or related areas.” (Philippe G. LeFloch, Mathematical Reviews, Issue 2011 i)

“The third edition of the famous book by C. M. Dafermos … devoted to the mathematical theory of hyperbolic conservation and balance laws. This masterly written book is, surely, the most entire exposition in the subject of conservation laws.”­­­ (Evgeniy Panov, Zentralblatt MATH, Vol. 1196, 2010)