© 2007

Hyperbolic Systems of Balance Laws

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

  • Pierangelo Marcati

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

Table of contents

  1. Front Matter
    Pages I-XII
  2. 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.


Profil discrete shock profiles hyperbolic conservation laws nonlinear hypebolic systems stability of shock waves vanishing viscosity

Authors and affiliations

  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA
  2. 2.Unité de mathématiques pures et appliquéesEcole Normale Supérieure de LyonLyon Cedex 07France
  3. 3.Department of MathematicsUniversity of North CarolinaChapel HillUSA
  4. 4.Department of MathematicsIndiana UniversityBloomington

Editors and affiliations

  • Pierangelo Marcati
    • 1
  1. 1.Department of Pure and Applied MathematicsUniversity of L'AquilaL'AquilaItaly

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
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-72186-4
  • eBook ISBN 978-3-540-72187-1
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XII, 356
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
    Classical and Continuum Physics
    Numerical Analysis
  • Buy this book on publisher's site