Hyperbolic Systems of Balance Laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003 (Lecture Notes in ... Notes in Mathematics, 1911, Band 1911) - Softcover

Bressan, Alberto

 
9783540721864: Hyperbolic Systems of Balance Laws: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003 (Lecture Notes in ... Notes in Mathematics, 1911, Band 1911)
Softcover
ISBN 10: 354072186X ISBN 13: 9783540721864
Verlag: Springer, 2007

Inhaltsangabe

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.

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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.

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Verlag
Springer
Erscheinungsdatum
2007
Sprache
Englisch
ISBN 10 
354072186X
ISBN 13 
9783540721864
Einband
Taschenbuch
Anzahl der Seiten
372
Kontakt zum Hersteller
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Poststr. 9
Darmstadt
64293
Deutschland

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