Hyperbolic Equations and Frequency Interactions (Ias/Park City Mathematics Series, V. 5) - Luis A. Caffarelli, Caffarelli, Luis A, E, Weinan (1998)
ISBN 0821805924
Subject Abelian groups; Differential equations, Partial; Geometrical optics - Mathematics; Schro¨dinger equation; Wavelets (Mathematics)
Publisher American Mathematical Society
Publication Date September 1998
Format Hardcover (267 x 191 mm)
Language e
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.

Personal Details
Collection Status In Collection
Index 268
Read It Yes
Links Amazon US
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Product Details
LoC Classification QC381.H96 vol 5 1999
Dewey 515/.353
Cover Price $76.00
No. of Pages 466
Lecture notes from a summer program held in Park City, Utah, July 9-29, 1995.