C.I.M.E. Foundation Subseries

Hyperbolic Systems of Balance Laws

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

Authors: Bressan, A., Serre, D., Williams, M., Zumbrun, K.

Editors: Marcati, Pierangelo (Ed.)

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  • ISBN 978-3-540-72187-1
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Softcover $79.95
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  • ISBN 978-3-540-72186-4
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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.

Table of contents (4 chapters)

  • BV Solutions to Hyperbolic Systems by Vanishing Viscosity

    Bressan, Alberto

    Pages 1-77

  • Discrete Shock Profiles: Existence and Stability

    Serre, Denis

    Pages 79-158

  • Stability of Multidimensional Viscous Shocks

    Williams, Mark

    Pages 159-227

  • Planar Stability Criteria for Viscous Shock Waves of Systems with Real Viscosity

    Zumbrun, Kevin

    Pages 229-326

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-540-72187-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-540-72186-4
  • 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 Balance Laws
Book Subtitle
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
Authors
Editors
  • Pierangelo Marcati
Series Title
C.I.M.E. Foundation Subseries
Series Volume
1911
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-72187-1
DOI
10.1007/978-3-540-72187-1
Softcover ISBN
978-3-540-72186-4
Edition Number
1
Number of Pages
XII, 356
Topics