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Applied Mathematical Sciences

Front Tracking for Hyperbolic Conservation Laws

Authors: Holden, Helge, Risebro, Nils Henrik

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  • Contains a lot of theorems, with full proofs, a true piece of mathematical Analysis
  • Offers a detailed, rigorous and self-contained presentation of the theory of hyperbolic conservation laws from the basic theory to the forefront of research
  • Treats the scalar case as well as the case of systems of conservation laws
  • Displays a lot of details and information about numerical approximation for the Cauchy Problem
  • Suitable for graduate courses in PDEs and numerical analysis
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  • ISBN 978-3-662-47507-2
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About this Textbook

This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions and the detailed solution of the Riemann problem for the Euler equations.

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included.

From the reviews of the first edition:

"It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet

"I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc.

"Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

About the authors

Helge Holden is professor of mathematics at the Norwegian University of Science and Technology and an adjunct professor at the Center of Mathematics for Applications, part of the University of Oslo.  He has done extensive research in stochastic analysis, in particular in its application to flow in porous media.

Nils Henrik Risebro is professor of mathematics at the University of Oslo. His research interests are mainly nonlinear partial differential equations and numerical methods for these. He has also worked on conservation laws with discontinuous coefficients in a variety of applications.

Reviews

“This is the 2nd edition of the famous book … devoted to the modern theory of hyperbolic conservation laws. … The book is well written, well illustrated (it contains even cartoons) and may be recommended not only to experienced specialists in conservation laws but also to students specialized in this field.” (Evgeniy Panov, zbMATH 1346.35004, 2016)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-662-47507-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-662-47506-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-662-56899-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Front Tracking for Hyperbolic Conservation Laws
Authors
Series Title
Applied Mathematical Sciences
Series Volume
152
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-47507-2
DOI
10.1007/978-3-662-47507-2
Hardcover ISBN
978-3-662-47506-5
Softcover ISBN
978-3-662-56899-6
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XIV, 517
Number of Illustrations
1240 illustrations in colour
Topics

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