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Front Tracking for Hyperbolic Conservation Laws

  • Textbook
  • Oct 2011

Overview

Authors:
  1. Helge Holden

    1. of Science and Technology, Dept. of Mathematics, Norwegian University, Trondheim, Norway

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    You can also search for this author in PubMed   Google Scholar

  2. Nils H. Risebro

    1. , Department of Mathematics, University of Oslo, Blindern, Norway

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    You can also search for this author in PubMed   Google Scholar

  • Contains a lot of theorems, with full proofs, a true piece of mathematical analysis
  • Offers a detailed, rigorous, and self-contained presentation of the theory of hyperbolic conservation laws from the basic theory to the forefront of research
  • Displays a lot of details and information about numerical approximation for the Cauchy problem
  • Suitable for graduate courses in PDEs and numerical analysis
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied Mathematical Sciences (AMS, volume 152)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Helge Holden, Nils Henrik Risebro
    Pages 1-21

  3. Scalar Conservation Laws

    • Helge Holden, Nils Henrik Risebro
    Pages 23-62

  4. A Short Course in Difference Methods

    • Helge Holden, Nils Henrik Risebro
    Pages 63-116

  5. Multidimensional Scalar Conservation Laws

    • Helge Holden, Nils Henrik Risebro
    Pages 117-162

  6. The Riemann Problem for Systems

    • Helge Holden, Nils Henrik Risebro
    Pages 163-204

  7. Existence of Solutions of the Cauchy Problem for Systems

    • Helge Holden, Nils Henrik Risebro
    Pages 205-231

  8. Well-Posedness of the Cauchy Problem for Systems

    • Helge Holden, Nils Henrik Risebro
    Pages 233-286

  9. Back Matter

    Pages 287-361
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Keywords

About this book

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.

Authors and Affiliations

  • of Science and Technology, Dept. of Mathematics, Norwegian University, Trondheim, Norway

    Helge Holden

  • , Department of Mathematics, University of Oslo, Blindern, Norway

    Nils H. Risebro

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