Multi-dimensional Hyperbolic Partial Differential Equations: First-order Systems and Applications

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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.

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Editorial Reviews

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"This is an excellent book."—Mathematical Reviews
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Product Details

  • ISBN-13: 9780199211234
  • Publisher: Oxford University Press
  • Publication date: 1/18/2007
  • Series: Oxford Mathematical Monographs Series
  • Pages: 536
  • Product dimensions: 9.30 (w) x 6.20 (h) x 1.30 (d)

Meet the Author

Universite Claude Bernard Lyon I

ENS de Lyon

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Table of Contents

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
A. Basic calculus results
B. Fourier and Laplace analysis
C. Pseudo/para-differential calculus

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