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Multi-Dimensional Hyperbolic Partial Differential Equations: First-Order Systems and Applications (Oxford Mathematical Monographs)

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Multi-Dimensional Hyperbolic Partial Differential Equations: First-Order Systems and Applications (Oxford Mathematical Monographs) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

These equations have been all the rage for over half a century, say Benzone-Gavage (U. Claude Bernard Lyon I) and Serre (ENS de Lyon), but little work has been done on genuinely multi-dimensional hyperbolic problems. Without pretending to cover the most recent results, they offer a broad view of the current status of the multi-dimensional dimension, emphasizing problems in which modern tools of analysis have proved useful. A large part of the study is devoted to initial boundary value problems, which can only be dealt with by using symbolic symmetrizers, and thus require pseudo-differential or even para-differential calculus. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)

Table of Contents

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

Product Details

ISBN:
9780199211234
Author:
Benzoni-gavage, Sylvie
Publisher:
Oxford University Press, USA
Author:
Benzoni-Gavage, Sylvie
Author:
Serre, Denis
Author:
null, Denis
Author:
null, Sylvie
Subject:
Differential Equations
Subject:
Differential Equations - Partial Differential Equations
Subject:
Differential equations, partial
Subject:
Differential equations, Hyperbolic
Subject:
Mathematics | Applied Mathematics
Subject:
Mathematics-Differential Equations
Series:
Oxford Mathematical Monographs
Publication Date:
20070131
Binding:
HARDCOVER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
536
Dimensions:
6.2 x 9.3 x 1.3 in 1.963 lb

Related Subjects

Education » Phonics
Science and Mathematics » Mathematics » Differential Equations

Multi-Dimensional Hyperbolic Partial Differential Equations: First-Order Systems and Applications (Oxford Mathematical Monographs) New Hardcover
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