Hyperbolic Partial Differential Equations and Geometric Optics

Rauch, Jeffrey

ISBN 10: 0821872915 / ISBN 13: 9780821872918

Edité par Amer Mathematical Society, 2012

373 pages. 10.25x7.25x1.00 inches. In Stock. N° de réf. du vendeur 0821872915

Synopsis :

This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed.

Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations.

One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader.

The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.

À propos de l?auteur: Jeffrey Rauch, University of Michigan, Ann Arbor, MI, USA

Détails bibliographiques

Titre : Hyperbolic Partial Differential Equations ...
Éditeur : Amer Mathematical Society
Date d'édition : 2012
Reliure : Hardcover
Etat : Brand New