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  • © 2007

Hyperbolic Systems of Balance Laws

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003

Authors:

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1911)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XII
  2. Stability of Multidimensional Viscous Shocks

    • Mark Williams
    Pages 159-227
  3. Back Matter

    Pages 327-356

About this book

The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case.

Keywords

  • Profil
  • discrete shock profiles
  • hyperbolic conservation laws
  • nonlinear hypebolic systems
  • stability of shock waves
  • vanishing viscosity
  • partial differential equations

Authors, Editors and Affiliations

  • Department of Pure and Applied Mathematics, University of L'Aquila, L'Aquila, Italy

    Pierangelo Marcati

  • Department of Mathematics, Penn State University, University Park, USA

    Alberto Bressan

  • Unité de mathématiques pures et appliquées, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France

    Denis Serre

  • Department of Mathematics, University of North Carolina, Chapel Hill, USA

    Mark Williams

  • Department of Mathematics, Indiana University, Bloomington

    Kevin Zumbrun

Bibliographic Information

  • Book Title: Hyperbolic Systems of Balance Laws

  • Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003

  • Authors: Alberto Bressan, Denis Serre, Mark Williams, Kevin Zumbrun

  • Editors: Pierangelo Marcati

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-72187-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-72186-4Published: 06 June 2007

  • eBook ISBN: 978-3-540-72187-1Published: 26 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 356

  • Topics: Differential Equations, Classical and Continuum Physics, Numerical Analysis

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions