Grundlehren der mathematischen Wissenschaften

Hyperbolic Conservation Laws in Continuum Physics

Authors: Dafermos, Constantine M.

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  • The author is unquestionably the greatest authority on the subject as well as a masterly writer
  • The book will immediately find a following as both an introduction to the field and a reference for research
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About this book

The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi­ ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva­ tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper­ bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.

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)


Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-3-662-22019-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Hyperbolic Conservation Laws in Continuum Physics
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
325
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-22019-1
DOI
10.1007/978-3-662-22019-1
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XVI, 446
Number of Illustrations
5 b/w illustrations
Topics