✦ LIBER ✦

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, Pierangelo Marcati

Book ID: 127419617
Publisher: Springer; Fondazione C.I.M.E
Year: 2007
Tongue: English
Weight: 2 MB
Series: Lecture notes in mathematics 1911
Edition: 1
Category: Library
City: Berlin; New York :, Firenze
ISBN-13: 9783540721864
ISSN: 0075-8434

No coin nor oath required. For personal study only.

✦ Synopsis

The present Cime volume includes 4 lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan’s notes start with an extensive review 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’ lectures describe the stability of multidimensional viscous shocks. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, and necessary and sufficient conditions for nonlinear stability.

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