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Includes supplementary material: sn.pub/extras
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)
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Front Matter
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Back Matter
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
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Department of Pure and Applied Mathematics, University of L'Aquila, L'Aquila, Italy
Pierangelo Marcati
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Department of Mathematics, Penn State University, University Park, USA
Alberto Bressan
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Unité de mathématiques pures et appliquées, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France
Denis Serre
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Department of Mathematics, University of North Carolina, Chapel Hill, USA
Mark Williams
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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