Multi-Dimensional Hyperbolic Partial Differential Equations

First-Order Systems and Applications
Erscheinungsjahr 2006
ISBN: 978-0-19-921123-4
Verlag: OUP Oxford

Buch, Englisch, 536 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 963 g

Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids.

With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Autoren/Hrsg.

Benzoni-Gavage, Sylvie

Serre, Denis

Fachgebiete

• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Naturwissenschaften Physik Physik Allgemein

Inhaltsverzeichnis

- Preface

- Introduction

- Notations

- The linear Cauchy problem

- 1: Linear Cauchy problem with constant coefficients

- 2: Linear Cauchy problem with variable coefficients

- The linear initial boundary value problem

- 3: Friedrichs symmetric dissipative IBVPs

- 4: Initial boundary value problem in a half-space with constant coefficients

- 5: Construction of a symmetrizer under (UKL)

- 6: The characteristic IBVP

- 7: The homogeneous IBVP

- 8: A classification of linear IBVPs

- 9: Variable coefficients initial boundary value problems

- Nonlinear problems

- 10: The Cauchy problem for quasilinear systems

- 11: The mixed problem for quasilinear systems

- 12: Persistence of multidimensional shocks

- Applications to gas dynamics

- 13: The Euler equations for real fluids

- 14: Boundary conditions for Euler equations

- 15: Shock stability in gas dynamics

- Appendix

- A: Basic calculus results

- B: Fourier and Laplace analysis

- C: Pseudo/para-differential calculus

- Bibliography

- Index