Overview
- 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
Part of the book series: Applied Mathematical Sciences (AMS, volume 152)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)
Authors and Affiliations
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.
Bibliographic Information
Book Title: Front Tracking for Hyperbolic Conservation Laws
Authors: Helge Holden, Nils Henrik Risebro
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-662-47507-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-47506-5Published: 18 December 2015
Softcover ISBN: 978-3-662-56899-6Published: 21 March 2019
eBook ISBN: 978-3-662-47507-2Published: 10 December 2015
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 2
Number of Pages: XIV, 517
Number of Illustrations: 1240 illustrations in colour
Topics: Applications of Mathematics, Numerical Analysis, Theoretical, Mathematical and Computational Physics, Mathematical and Computational Engineering