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Hyperbolic Systems of Balance Laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14–21, 2003

✍ Scribed by Alberto Bressan, Denis Serre, Mark Williams, Kevin Zumbrun (auth.), Pierangelo Marcati (eds.)

Book ID
127447362
Publisher
Springer
Year
2007
Tongue
English
Weight
3 MB
Edition
1
Category
Library
ISBN
3540721878

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Subjects

Numerical Analysis

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