Hyperbolic Partial Differential Equations - Brossura

Lax, Peter D.

Brossura

ISBN 10: 0821835769 ISBN 13: 9780821835760

Casa editrice: Amer Mathematical Society, 2006

Riassunto

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2006
• ISBN 10: 0821835769
• ISBN 13: 9780821835760
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 217