Multi-dimensional hyperbolic partial differential equations
First-order systems and applications
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher OUP Oxford
- Date of Publication 23 November 2006
- ISBN 9780199211234
- Binding Hardback
- No. of pages536 pages
- Size 240x164x34 mm
- Weight 893 g
- Language English 0
Categories
Short description:
Authored by leading scholars, this text presents the state of the art in multi-dimensional hyperbolic PDEs, with an emphasis on problems in which modern tools of analysis are used. Ordered in sections of gradually increasing difficulty and with an extensive bibliography, the text is ideal for graduates and researchers in applied mathematics.
MoreLong description:
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.
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.
Table of Contents:
Preface
Introduction
Notations
The linear Cauchy problem
Linear Cauchy problem with constant coefficients
Linear Cauchy problem with variable coefficients
The linear initial boundary value problem
Friedrichs symmetric dissipative IBVPs
Initial boundary value problem in a half-space with constant coefficients
Construction of a symmetrizer under (UKL)
The characteristic IBVP
The homogeneous IBVP
A classification of linear IBVPs
Variable coefficients initial boundary value problems
Nonlinear problems
The Cauchy problem for quasilinear systems
The mixed problem for quasilinear systems
Persistence of multidimensional shocks
Applications to gas dynamics
The Euler equations for real fluids
Boundary conditions for Euler equations
Shock stability in gas dynamics
Appendix
Basic calculus results
Fourier and Laplace analysis
Pseudo/para-differential calculus
Bibliography
Index
