ENGLISH

Hyperbolic systems of balance laws: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003

By Denis Serre , Alberto Bressan , Mark Williams , Kevin Zumbrun , Pierangelo Marcati

Book information

Publisher
Springer; Fondazione C.I.M.E
Year
2007
ISBN
354072186X, 9783540721864
ISSN
0075-8434
Open Library ID
OL14562419M
Language
english
Format
PDF
Filesize
2 MB (2467337 bytes)
Series
Lecture notes in mathematics 1911
Edition
1
Pages
366\366
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

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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