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Microlocal Analysis and Nonlinear Waves

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Michael Beals

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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  2. Richard B. Melrose

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  3. Jeffrey Rauch

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

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 30)

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Table of contents (14 papers)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. On the Interactions of Conormal Waves for Semilinear Wave Equations

    • Antônio Sá Barreto
    Pages 1-7

  3. Regularity of Nonlinear Waves Associated with a Cusp

    • Michael Beals
    Pages 9-27

  4. Evolution of a Punctual Singularity in an Eulerian Flow

    • Jean Yves Chemin
    Pages 29-36

  5. Water Waves, Hamiltonian Systems and Cauchy Integrals

    • Walter Craig
    Pages 37-45

  6. Infinite Gain of Regularity for Dispersive Evolution Equations

    • W. Craig, T. Kappeler, W. Strauss
    Pages 47-50

  7. On the Fully Non-Linear Cauchy Problem with Small Data. II.

    • Lars Hörmander
    Pages 51-81

  8. Interacting Weakly Nonlinear Hyperbolic and Dispersive Waves

    • John K. Hunter
    Pages 83-111

  9. Nonlinear Resonance Can Create Dense Oscillations

    • Jean-Luc Joly, Jeffrey Rauch
    Pages 113-123

  10. Lower Bounds of the Life-Span of Small Classical Solutions for Nonlinear Wave Equations

    • Li Ta-Tsien
    Pages 125-136

  11. Propagation of Stronger Singularities of Solutions to Semilinear Wave Equations

    • Liu Linqi
    Pages 137-154

  12. Conormality, Cusps and Non-Linear Interaction

    • Richard B. Melrose
    Pages 155-166

  13. Quasimodes for the Laplace Operator and Glancing Hypersurfaces

    • Georgi S. Popov
    Pages 167-178

  14. A Decay Estimate for the Three-Dimensional Inhomogeneous Klein-Gordon Equation and Global Existence for Nonlinear Equations

    • Thomas C. Sideris
    Pages 179-183

  15. Interaction of Singularities and Propagation into Shadow Regions in Semilinear Boundary Problems

    • Mark Williams
    Pages 185-199
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Keywords

About this book

This IMA Volume in Mathematics and its Applications MICROLOCAL ANALYSIS AND NONLINEAR WAVES is based on the proceedings of a workshop which was an integral part of the 1988- 1989 IMA program on "Nonlinear Waves". We thank Michael Beals, Richard Melrose and Jeffrey Rauch for organizing the meeting and editing this proceedings volume. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE Microlocal analysis is natural and very successful in the study of the propagation of linear hyperbolic waves. For example consider the initial value problem Pu = f E e'(RHd), supp f C {t ;::: O} u = 0 for t < o. If P( t, x, Dt,x) is a strictly hyperbolic operator or system then the singular support of f gives an upper bound for the singular support of u (Courant-Lax, Lax, Ludwig), namely singsupp u C the union of forward rays passing through the singular support of f.

Editors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Michael Beals

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Richard B. Melrose

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

    Jeffrey Rauch

Bibliographic Information

  • Book Title: Microlocal Analysis and Nonlinear Waves

  • Editors: Michael Beals, Richard B. Melrose, Jeffrey Rauch

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-9136-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1991

  • Softcover ISBN: 978-1-4613-9138-8Published: 21 December 2011

  • eBook ISBN: 978-1-4613-9136-4Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XIII, 199

  • Topics: Analysis

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