Hyperbolic Conservation Laws in Continuum Physics / Edition 3

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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

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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9783642242427
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/6/2011
  • Series: Grundlehren der mathematischen Wissenschaften Series , #325
  • Edition description: Softcover reprint of hardcover 3rd ed. 2010
  • Edition number: 3
  • Pages: 710
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.49 (d)

Table of Contents

Balance Laws.- to Continuum Physics.- Hyperbolic Systems of Balance Laws.- The Cauchy Problem.- Entropy and the Stability of Classical Solutions.- The Theory for Scalar Conservation Laws.- Hyperbolic Systems of Balance Laws in One-Space Dimension.- Admissible Shocks.- Admissible Wave Fans and the Riemann Problem.- Generalized Characteristics.- Genuinely Nonlinear Scalar Conservation Laws.- Genuinely Nonlinear Systems of Two Conservation Laws.- The Random Choice Method.- The Front Tracking Method and Standard Riemann Semigroups.- Construction of Solutions by the Vanishing Viscosity Method.- Compensated Compactness.- Conservation Laws in Two Space Dimensions.
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