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Hyperbolic Equations and Frequency Interactions
 
Edited by: Luis Caffarelli New York University-Courant Institute of Mathematical Sciences, New York, NY
Weinan E New York University-Courant Institute of Mathematical Sciences, New York, NY
A co-publication of the AMS and IAS/Park City Mathematics Institute
Hyperbolic Equations and Frequency Interactions
Hardcover ISBN:  978-0-8218-0592-3
Product Code:  PCMS/5
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-3904-0
Product Code:  PCMS/5.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-0592-3
eBook: ISBN:  978-1-4704-3904-0
Product Code:  PCMS/5.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
Hyperbolic Equations and Frequency Interactions
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Hyperbolic Equations and Frequency Interactions
Edited by: Luis Caffarelli New York University-Courant Institute of Mathematical Sciences, New York, NY
Weinan E New York University-Courant Institute of Mathematical Sciences, New York, NY
A co-publication of the AMS and IAS/Park City Mathematics Institute
Hardcover ISBN:  978-0-8218-0592-3
Product Code:  PCMS/5
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-3904-0
Product Code:  PCMS/5.E
List Price: $112.00
MAA Member Price: $100.80
AMS Member Price: $89.60
Hardcover ISBN:  978-0-8218-0592-3
eBook ISBN:  978-1-4704-3904-0
Product Code:  PCMS/5.B
List Price: $237.00 $181.00
MAA Member Price: $213.30 $162.90
AMS Member Price: $189.60 $144.80
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 51999; 466 pp
    MSC: Primary 35; 42; 74; 76;

    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.

    Readership

    Graduate students and research mathematicians working in partial differential equations.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Nonlinear Schrödinger equations
    • Harmonic analysis, wavelets and applications
    • Lectures on stability and instability of an ideal fluid
    • Waves and transport
    • Lectures on geometric optics
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 51999; 466 pp
MSC: Primary 35; 42; 74; 76;

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.

Readership

Graduate students and research mathematicians working in partial differential equations.

  • Chapters
  • Introduction
  • Nonlinear Schrödinger equations
  • Harmonic analysis, wavelets and applications
  • Lectures on stability and instability of an ideal fluid
  • Waves and transport
  • Lectures on geometric optics
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.