Hyperbolic Equations and Frequency Interactions
( IAS/Park City Mathematics Series )
Publication series ：IAS/Park City Mathematics Series
Author： Luis Caffarelli;Weinan E
Publisher： American Mathematical Society
Publication year： 2017
E-ISBN: 9781470439040
P-ISBN(Paperback): 9780821805923
Subject： O435 geometrical optics
Keyword： 暂无分类
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Hyperbolic Equations and Frequency Interactions
Description
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 toget
Chapter