Helge Holden & Nils Henrik Risebro 
Front Tracking for Hyperbolic Conservation Laws [PDF ebook] 

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, Math Sci Net"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.