Hyperbolic Partial Differential Equations

Lax, Peter D.

ISBN 10: 0821835769 / ISBN 13: 9780821835760

Verlag: American Mathematical Society, 2006

Pages intact with possible writing/highlighting. Binding strong with minor wear. Dust jackets/supplements may not be included. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good. Bestandsnummer des Verkäufers 57798567-6

Inhaltsangabe:

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.

Bibliografische Details

Titel: Hyperbolic Partial Differential Equations
Verlag: American Mathematical Society
Erscheinungsdatum: 2006
Einband: Softcover
Zustand: Very Good