Lectures in Mathematics. ETH Zürich

Hyperbolic Systems of Conservation Laws

The Theory of Classical and Nonclassical Shock Waves

Authors: LeFloch, Philippe G.

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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.

Table of contents (10 chapters)

  • Fundamental Concepts and Examples

    LeFloch, Philippe G.

    Pages 1-26

  • The Riemann Problem

    LeFloch, Philippe G.

    Pages 29-50

  • Diffusive-Dispersive Traveling Waves

    LeFloch, Philippe G.

    Pages 51-80

  • Existence Theory for the Cauchy Problem

    LeFloch, Philippe G.

    Pages 81-117

  • Continuous Dependence of Solutions

    LeFloch, Philippe G.

    Pages 118-136

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-0348-8150-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-7643-6687-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hyperbolic Systems of Conservation Laws
Book Subtitle
The Theory of Classical and Nonclassical Shock Waves
Authors
Series Title
Lectures in Mathematics. ETH Zürich
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8150-0
DOI
10.1007/978-3-0348-8150-0
Softcover ISBN
978-3-7643-6687-2
Edition Number
1
Number of Pages
X, 294
Topics