Front Tracking for Hyperbolic Conservation Laws

by Helge Holden (Author), Nils Henrik Risebro (Author)
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

From the Back Cover

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 Author
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.

Topics
Applications of Mathematics
Numerical Analysis
Theoretical, Mathematical and Computational Physics
Appl. Mathematics / Computational Methods of Engineering

More info and Hardcover at Springer

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