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Hyperbolic Systems of Conservation Laws

The Theory of Classical and Nonclassical Shock Waves

  • Book
  • © 2002

Overview

Authors:
  1. Philippe G. LeFloch

    1. Centre de Mathématiques Appliquées & Centre National de la Recherche Scientifique, Ecole Polytechnique, Palaiseau, France

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Part of the book series: Lectures in Mathematics. ETH Zürich (LM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Fundamental Concepts and Examples

    1. Fundamental Concepts and Examples

      • Philippe G. LeFloch
      Pages 1-26

  3. Scalar Conservation Laws

    1. Front Matter

      Pages 27-27
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    2. The Riemann Problem

      • Philippe G. LeFloch
      Pages 29-50

    3. Diffusive-Dispersive Traveling Waves

      • Philippe G. LeFloch
      Pages 51-80

    4. Existence Theory for the Cauchy Problem

      • Philippe G. LeFloch
      Pages 81-117

    5. Continuous Dependence of Solutions

      • Philippe G. LeFloch
      Pages 118-136

  4. Systems of Conservation Laws

    1. Front Matter

      Pages 137-137
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    2. The Riemann Problem

      • Philippe G. LeFloch
      Pages 139-166

    3. Classical Entropy Solutions of the Cauchy Problem

      • Philippe G. LeFloch
      Pages 167-187

    4. Nonclassical Entropy Solutions of the Cauchy Problem

      • Philippe G. LeFloch
      Pages 188-211

    5. Continuous Dependence of Solutions

      • Philippe G. LeFloch
      Pages 212-240

    6. Uniqueness of Entropy Solutions

      • Philippe G. LeFloch
      Pages 241-258

  5. Back Matter

    Pages 259-294
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Keywords

About this book

This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would like to thank the faculty of the Mathematics Department, and especially Rolf Jeltsch and Michael Struwe, for giving me such a great opportunity to deliver the lectures in a very stimulating environment. Part of this material was also taught earlier as an advanced graduate course at the Ecole Poly technique (Palaiseau) during the years 1995-99, at the Instituto Superior Tecnico (Lisbon) in the Spring 1998, and at the University of Wisconsin (Madison) in the Fall 1998. This project started in the Summer 1995 when I gave a series of lectures at the Tata Institute of Fundamental Research (Bangalore). One main objective in this course is to provide a self-contained presentation of the well-posedness theory for nonlinear hyperbolic systems of first-order partial differential equations in divergence form, also called hyperbolic systems of con­ servation laws. Such equations arise in many areas of continuum physics when fundamental balance laws are formulated (for the mass, momentum, total energy . . . of a fluid or solid material) and small-scale mechanisms can be neglected (which are induced by viscosity, capillarity, heat conduction, Hall effect . . . ). Solutions to hyper­ bolic conservation laws exhibit singularities (shock waves), which appear in finite time even from smooth initial data.

Authors and Affiliations

  • Centre de Mathématiques Appliquées & Centre National de la Recherche Scientifique, Ecole Polytechnique, Palaiseau, France

    Philippe G. LeFloch

Bibliographic Information

  • Book Title: Hyperbolic Systems of Conservation Laws

  • Book Subtitle: The Theory of Classical and Nonclassical Shock Waves

  • Authors: Philippe G. LeFloch

  • Series Title: Lectures in Mathematics. ETH Zürich

  • DOI: https://doi.org/10.1007/978-3-0348-8150-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2002

  • Softcover ISBN: 978-3-7643-6687-2Published: 01 July 2002

  • eBook ISBN: 978-3-0348-8150-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 294

  • Topics: Analysis, Partial Differential Equations

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