Multi-dimensional Hyperbolic Partial Differential Equations

First-order systems and applications

Sylvie Benzoni-Gavage, Denis Serre - Collection Oxford Mathematical Monographs

512 pages, parution le 12/12/2006

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Résumé

Authored by leading academics
Comprehensive, self-contained work
Adopts an original approach, presents new results, and fills gaps in proofs of important theorems
Extensive bibliography, including classical and recent papers in both PDE analysis and in applications (mainly to gas dynamics)

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.

Readership: Graduates and researchers in Applied Mathematics

L'auteur - Sylvie Benzoni-Gavage

Sylvie Benzoni-Gavage, Université Claude Bernard Lyon I, France

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L'auteur - Denis Serre

Denis Serre is Professor of Mathematics at École Normale Supérieure de Lyon and a former member of the Institut Universitaire de France. He is a member of numerous editorial boards and the author of "Systems of Conservation Laws" (Cambridge University Press 2000). With S. Benzoni-Gavage, he is the co-author of "Multi-Dimensional Hyperbolic Partial Differential Equations. First Order Systems and Applications" (Oxford University Press 2007). With S. Friedlander, he has co-edited four volumes of a "Handbook of Mathematical Fluid Dynamics" (Elsevier 2002--2007). The first edition of the present book is a translation of the original French edition, "Les Matrices: Théorie et Pratique", published by Dunod (2001).

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Sommaire

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

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	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Sylvie Benzoni-Gavage, Denis Serre
Collection	Oxford Mathematical Monographs
Parution	12/12/2006
Nb. de pages	512
Format	16,5 x 24
Couverture	Relié
Poids	890g
Intérieur	Noir et Blanc
EAN13	9780199211234
ISBN13	978-0-19-921123-4