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

Alberto Bressan (u. a.)

ISBN 10: 354072186X / ISBN 13: 9783540721864

Published by Springer, 2007

About this Item

Hyperbolic Systems of Balance Laws | Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003 | Alberto Bressan (u. a.) | Taschenbuch | Lecture Notes in Mathematics | xii | Englisch | 2007 | Springer | EAN 9783540721864 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 102056630

Bibliographic Details

• Title: Hyperbolic Systems of Balance Laws | Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
• Publisher: Springer
• Publication Date: 2007
• Language: English
• ISBN 10: 354072186X
• ISBN 13: 9783540721864
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 21D millimeters 235 millimeters width by 155 millimeters height by 21 millimeters depth
• Weight: 563 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

From the Back Cover

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.