Holden H., Risebro N.H. Front Tracking for Hyperbolic Conservation Laws

Springer-Verlag Berlin Heidelberg 2011. — (Applied Mathematical Sciences 152). — 362 pp. — ISBN: 978-3-642-23910-6 (Print) 978-3-642-23911-3 (Online).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:
"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.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
Displays a lot of details and information about numerical approximation for the Cauchy problem
Suitable for graduate courses in PDEs and numerical analysisScalar Conservation Laws
A Short Course in Difference Methods
Multidimensional Scalar Conservation Laws
The Riemann Problem for Systems
Existence of Solutions of the Cauchy Problem for Systems
Well-Posedness of the Cauchy Problem for Systems.