Author | Holden, Helge. author |
---|---|

Title | Front Tracking for Hyperbolic Conservation Laws [electronic resource] / by Helge Holden, Nils Henrik Risebro |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002 |

Connect to | http://dx.doi.org/10.1007/978-3-642-56139-9 |

Descript | XII, 264 p. 2 illus. online resource |

SUMMARY

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

CONTENT

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