© 2015

Front Tracking for Hyperbolic Conservation Laws


Part of the Applied Mathematical Sciences book series (AMS, volume 152)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Helge Holden, Nils Henrik Risebro
    Pages 1-51
  3. Helge Holden, Nils Henrik Risebro
    Pages 53-94
  4. Helge Holden, Nils Henrik Risebro
    Pages 95-169
  5. Helge Holden, Nils Henrik Risebro
    Pages 171-221
  6. Helge Holden, Nils Henrik Risebro
    Pages 223-281
  7. Helge Holden, Nils Henrik Risebro
    Pages 283-312
  8. Helge Holden, Nils Henrik Risebro
    Pages 313-366
  9. Helge Holden, Nils Henrik Risebro
    Pages 367-426
  10. Back Matter
    Pages 427-517

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 excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.


conservation laws front tracking hyperbolic partial differential equations xxx xxx

Authors and affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of MathematicsUniversity of OsloOsloNorway

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


“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)