Hyperbolic Conservation Laws in Continuum Physics: No. 325 (Die Grundlehren der Mathematischen Wissenschaften) - Hardcover

Dafermos, Constantine M.

Hardcover

ISBN 10: 3642040470 ISBN 13: 9783642040474

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2009

Synopsis

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

About this title

Review:

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)

From the Back Cover:

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

About this edition

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 2009
• ISBN 10: 3642040470
• ISBN 13: 9783642040474
• Binding: Hardcover
• Edition number: 3
• Number of pages: 745