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Front Tracking for Hyperbolic Conservation Laws [electronic resource] / by Helge Holden, Nils H. Risebro.

By: Holden, Helge [author.].
Contributor(s): Risebro, Nils H [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Applied Mathematical Sciences: 152Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: XII, 361 p. 40 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642239113.Subject(s): Mathematics | Numerical analysis | Engineering mathematics | Mathematics | Applications of Mathematics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of EngineeringDDC classification: 519 Online resources: Click here to access online
Contents:
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 -- Total Variations, Compactness etc. -- The Method of Vanishing Viscosity -- Answers and Hints -- References -- Index.    .
In: Springer eBooksSummary: 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.
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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 -- Total Variations, Compactness etc. -- The Method of Vanishing Viscosity -- Answers and Hints -- References -- Index.    .

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.

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