Front Tracking for Hyperbolic Conservation Laws [electronic resource] / by Helge Holden, Nils Henrik Risebro.
Contributor(s): Risebro, Nils Henrik [author.] | SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 152Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015Edition: 2nd ed. 2015Description: XIV, 517 p. 1240 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783662475072Subject(s): Mathematics | Applied mathematics | Engineering mathematics | Numerical analysis | Physics | Mathematics | Applications of Mathematics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: T57-57.97Online resources: Click here to access online
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Preface -- Introduction -- Scalar Conservation Laws -- A Short Course in Difference Methods -- Multidimensional Scalar Conservation Laws -- The Riemann Problem for Systems -- Existence of Solutions of the Cauchy Problem -- Well-Posedness of the Cauchy Problem -- Conservation Laws with Discontinuous Flux Functions -- Total Variation, Compactness etc -- The Method of Vanishing Viscosity -- Answers and Hints -- Index.
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.