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Singularities and Oscillations

  • Conference proceedings
  • © 1997

Overview

Editors:
  1. Jeffrey Rauch

    1. Department of Mathematics, University of Michigan, Ann Arbor, USA

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  2. Michael Taylor

    1. Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 91)

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Table of contents (7 papers)

  1. Front Matter

    Pages i-ix
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  2. Observation and Control of Elastic Waves

    • Claude Bardos, Tawfik Masrour, Frederic Tatout
    Pages 1-16

  3. Modeling the Dispersion of Light

    • Phillipe Donnat, Jeffrey Rauch
    Pages 17-35

  4. Singularities and Oscillations in a Nonlinear Variational Wave Equation

    • Robert T. Glassey, John K. Hunter, Yuxi Zheng
    Pages 37-60

  5. Viscous Boundary Layers and High Frequency Oscillations

    • Olivier Gues
    Pages 61-77

  6. Nonlinear Oscillations and Caustics

    • J. L. Joly, G. Métivier, J. Rauch
    Pages 79-95

  7. Microlocal Analysis on Morrey Spaces

    • Michael E. Taylor
    Pages 97-135

  8. Nonlinear Geometric Optics for Reflecting and Glancing Oscillations

    • Mark Williams
    Pages 137-151

  9. Back Matter

    Pages 153-158
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Keywords

About this book

This IMA Volume in Mathematics and its Applications SINGULARITIES AND OSCILLATIONS is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering. " We would like to thank Joseph Keller, Jeffrey Rauch, and Michael Taylor for their excellent work as organizers of the meeting. We would like to express our further gratitude to Rauch and Taylor, who served as editors of the proceedings. We also take this opportunity to thank the National Science Foun­ dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. Avner Friedman Robert Gulliver v PREFACE Thestudyofsingularitiesand oscillationsofwaves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume con­ tains a multiplicity of approaches brought to bear on problems varying from the formation ofcaustics and the propagation ofwaves at a boundary to the examination ofviscous boundary layers. There is an examination of the foundations of the theory of high-frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis.

Editors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Jeffrey Rauch

  • Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, USA

    Michael Taylor

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