Microlocal Analysis and Nonlinear Waves

✍ Scribed by Antônio Sá Barreto (auth.), Michael Beals, Richard B. Melrose, Jeffrey Rauch (eds.)

• Publisher: Springer-Verlag New York
• Year: 1991
• Tongue: English
• Leaves: 204
• Series: The IMA Volumes in Mathematics and its Applications 30
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
On the Interactions of Conormal Waves for Semilinear Wave Equations....Pages 1-7
Regularity of Nonlinear Waves Associated with a Cusp....Pages 9-27
Evolution of a Punctual Singularity in an Eulerian Flow....Pages 29-36
Water Waves, Hamiltonian Systems and Cauchy Integrals....Pages 37-45
Infinite Gain of Regularity for Dispersive Evolution Equations....Pages 47-50
On the Fully Non-Linear Cauchy Problem with Small Data. II.....Pages 51-81
Interacting Weakly Nonlinear Hyperbolic and Dispersive Waves....Pages 83-111
Nonlinear Resonance Can Create Dense Oscillations....Pages 113-123
Lower Bounds of the Life-Span of Small Classical Solutions for Nonlinear Wave Equations....Pages 125-136
Propagation of Stronger Singularities of Solutions to Semilinear Wave Equations....Pages 137-154
Conormality, Cusps and Non-Linear Interaction....Pages 155-166
Quasimodes for the Laplace Operator and Glancing Hypersurfaces....Pages 167-178
A Decay Estimate for the Three-Dimensional Inhomogeneous Klein-Gordon Equation and Global Existence for Nonlinear Equations....Pages 179-183
Interaction of Singularities and Propagation into Shadow Regions in Semilinear Boundary Problems....Pages 185-199

✦ Subjects

Analysis