Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorHolden, Helge. author
TitleFront Tracking for Hyperbolic Conservation Laws [electronic resource] / by Helge Holden, Nils Henrik Risebro
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
Connect to
Descript XII, 264 p. 2 illus. online resource


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. "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


1 Introduction -- 1.1 Notes -- 2 Scalar Conservation Laws -- 2.1 Entropy Conditions -- 2.2 The Riemann Problem -- 2.3 Front Tracking -- 2.4 Existence and Uniqueness -- 2.5 Notes -- 3 A Short Course in Difference Methods -- 3.1 ConservativeMethods -- 3.2 Error Estimates -- 3.3 APriori Error Estimates -- 3.4 Measure-Valued Solutions -- 3.5 Notes -- 4 Multidimensional Scalar Conservation Laws -- 4.1 Dimensional SplittingMethods -- 4.2 Dimensional Splitting and Front Tracking -- 4.3 Convergence Rates -- 4.4 Operator Splitting: Diffusion -- 4.5 Operator Splitting: Source -- 4.6 Notes -- 5 The Riemann Problem for Systems -- 5.1 Hyperbolicity and Some Examples -- 5.2 Rarefaction Waves -- 5.3 The Hugoniot Locus: The Shock Curves -- 5.4 The Entropy Condition -- 5.5 The Solution of the Riemann Problem -- 5.6 Notes -- 6 Existence of Solutions of the Cauchy Problem -- 6.1 Front Tracking for Systems -- 6.2 Convergence -- 6.3 Notes -- 7 Well-Posedness of the Cauchy Problem -- 7.1 Stability -- 7.2 Uniqueness -- 7.3 Notes -- A Total Variation, Compactness, etc. -- A.1 Notes -- B The Method of Vanishing Viscosity -- B.1 Notes -- C Answers and Hints -- References

Mathematics Applied mathematics Engineering mathematics Numerical analysis Physics Mathematics Applications of Mathematics Numerical Analysis Theoretical Mathematical and Computational Physics Appl.Mathematics/Computational Methods of Engineering


Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network


facebook   instragram