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Grundlehren der mathematischen Wissenschaften

Hyperbolic Conservation Laws in Continuum Physics

Authors: Dafermos, Constantine M.

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  • Written by an author who is unquestionably an authority on the subject as well as a masterly writer
  • Revised, up-to-date fourth edition includes new material on the Euler equations of gas dynamics, and on hyperbolic balance laws with dissipative source, as well as new applications to elasticity and differential geometry
  • Features an expanded bibliography that now comprises close to two thousand titles
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eBook $84.99
$169.00 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-49451-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
$249.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-49449-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
$219.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-57011-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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.

This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles.

From the reviews of the 3rd edition:

"This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH

"A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews


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). 

Reviews

“This book is a contribution to the fields of mathematical analysis and partial differential equations and their broad interactions with various branches of applied mathematics and continuum physics, whose value cannot be overstated. … a useful resource for a variety of courses as well as an almost encyclopedic reference point for advanced researchers. … It is a great achievement that will influence the PDEs and mathematical analysis community for years to come.” (Marta Lewicka, Mathematical Reviews, November, 2017)

Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $84.99
$169.00 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-49451-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
$249.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-49449-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
$219.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-3-662-57011-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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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
2016
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-49451-6
DOI
10.1007/978-3-662-49451-6
Hardcover ISBN
978-3-662-49449-3
Softcover ISBN
978-3-662-57011-1
Series ISSN
0072-7830
Edition Number
4
Number of Pages
XXXVIII, 826
Number of Illustrations
52 b/w illustrations
Topics