IAS/Park City Mathematics Series
Volume: 5; 1999; 466 pp; Hardcover
MSC: Primary 35; 42; 74; 76;
Print ISBN: 978-0-8218-0592-3
Product Code: PCMS/5
List Price: $89.00
Individual Member Price: $71.20
Hyperbolic Equations and Frequency InteractionsShare this page
Edited by Luis Caffarelli; Weinan E
A co-publication of the AMS and IAS/Park City Mathematics Institute
The research topic for this IAS/PCMI Summer Session was nonlinear wave
phenomena. Mathematicians from the more theoretical areas of PDEs were brought
together with those involved in applications. The goal was to share ideas,
knowledge, and perspectives.
How waves, or “frequencies”, interact in nonlinear phenomena has been a central issue in many of the recent developments in pure and applied analysis. It is believed that wavelet theory—with its simultaneous localization in both physical and frequency space and its lacunarity—is and will be a fundamental new tool in the treatment of the phenomena.
Included in this volume are write-ups of the “general methods and tools” courses held by Jeff Rauch and Ingrid Daubechies. Rauch's article discusses geometric optics as an asymptotic limit of high-frequency phenomena. He shows how nonlinear effects are reflected in the asymptotic theory. In the article “Harmonic Analysis, Wavelets and Applications” by Daubechies and Gilbert the main structure of the wavelet theory is presented.
Also included are articles on the more “specialized” courses that were presented, such as “Nonlinear Schrödinger Equations” by Jean Bourgain and “Waves and Transport” by George Papanicolaou and Leonid Ryzhik. Susan Friedlander provides a written version of her lecture series “Stability and Instability of an Ideal Fluid”, given at the Mentoring Program for Women in Mathematics, a preliminary program to the Summer Session.
This Summer Session brought together students, fellows, and established mathematicians from all over the globe to share ideas in a vibrant and exciting atmosphere. This book presents the compelling results.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. NOTE: This discount does not apply to volumes in this series co-published with the Society for Industrial and Applied Mathematics (SIAM).
Table of Contents
Table of Contents
Hyperbolic Equations and Frequency Interactions
Graduate students and research mathematicians working in partial differential equations.