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Band 47

Advances in the Theory of Shock Waves

Aus der Reihe Progress in Nonlinear Differential Equations and Their Applications

97,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2012

Abbildungen

VIII, 520 p.

Herausgeber

Heinrich Freistühler + weitere

Verlag

Birkhäuser Boston

Seitenzahl

520

Maße (L/B/H)

23,5/15,5/2,9 cm

Gewicht

797 g

Auflage

Softcover reprint of the original 1st edition 2001

Sprache

Englisch

ISBN

978-1-4612-6655-6

Beschreibung

Portrait

Gathers recent insights in well posedness for conservation laws,
multidimensional shock stability, dissipation / relaxation phenomena,
and applications of shock wave theory to general relativity. Five self
-contained and interrelated articles, written by recognized experts in
the field, provide a survey of central themes in the modern
mathematical theory of shock waves. Combines the rigor of mathematical
analysis with attention to the physical origins and applications of
the field. Useful for graduate seminars or courses, or as a reference
text for mathematicians, physicists, and theoretically motivated
engineers.

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2012

Abbildungen

VIII, 520 p.

Herausgeber

Verlag

Birkhäuser Boston

Seitenzahl

520

Maße (L/B/H)

23,5/15,5/2,9 cm

Gewicht

797 g

Auflage

Softcover reprint of the original 1st edition 2001

Sprache

Englisch

ISBN

978-1-4612-6655-6

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: ProductSafety@springernature.com

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  • Produktbild: Advances in the Theory of Shock Waves
  • Produktbild: Advances in the Theory of Shock Waves
  • I. Well-Posedness Theory for Hyperbolic Systemsof Conservation Laws.- 1. Scalar conservation law.- 2. Glimm scheme.- 3. Wave tracing.- 4. Nonlinear functional.- II. Stability of Multidimensional Shocks.- 1. The uniform stability condition.- 2. The uniform stability estimates.- 3. Well posedness of the linearized shock front equations.- 4. The existence of multidimensional shocks.- 5. Stability of weak shocks.- III. Shock Wave Solutions of the Einstein Equations:A General Theory with Examples.- 1. Introduction.- 2. Solutions of the Einstein equations when the metricis only Lipschitz continuous across an interface.- 3. Matching an FRW to a TOV metric across a shock wave.- 4. A class of exact shock wave solutions of the Einstein equations — blast waves in GR.- 5. Cosmology with a shock wave.- 6. General comments on FRW–CTOV shock waves.- 7. The Oppenheimer–CSnyder limit and the solution for k = 0.- IV. Basic Aspects of Hyperbolic Relaxation Systems.- 1. Introduction.- 2. Relaxation criterion.- 3. The Chapman–CEnskog expansion.- 4. Admissible boundary conditions.- 5. Stability conditions.- 6. Typical examples.- 7. Moment closure systems.- 8. Discrete velocity kinetic models.- 9. Relaxation limits for smooth solutions.- 10. Shock structure problems.- V. Multidimensional Stability of Planar Viscous Shock Waves.- 1. Introduction.- 2. The Evans function and its low frequency limit.- 3. Necessary conditions for stability.- 4. Sufficient conditions for stability.- 5. Pointwise bounds for scalar equations.- 6. One-dimensional stability: the stability index.- 7. Discussion and open problems.- 8. Appendices: extensions and auxiliary calculations.