Lectures in a variety of topics were also given. They include: the Cauchy problem for strictly or weakly hyperbolic operators and their applications; semilinear, quasilinear or fully nonlinear equations; the Navier-Stokes and Schrodinger equations. Other topics discussed were the Sine-Gordon Hierarchy, oscillatory integrals and unique continuation problems, local solvability for differential or pseudodifferential operators, lower bounds of pseudodifferential systems. The most frequently occurring theme was perhaps the use of microlocal analysis, which is now a cornerstone in the study of linear and also nonlinear equations.

Table of Contents

The Global Existence of Smooth Solutions to Quasilinear Wave Equations, AVery Short Course – Serge Alinhac
Evolution Equations and Microlocal Analysis - Jean-Michel Bony
Necessary Conditions for the Well Posedness of the Cauchy Problem for Hyperbolic Systems – Antonio Bove and Tatsuo Nishitani
An Example of Singular Dynamics for the Nonlinear Schrodinger Equation on Bounded Domains - N. Burq, P. Gerard, and N. Tzvetkov
The Cauchy Problem for Some Nonstrictly Hyperbolic Equations with Nonregular Coefficients and its Applications – Ferruccio Colombini and Kunihiko Kajitani
The Cauchy Problem for Semilinear Second Order Equations with Finite Degeneracy – Ferruccio Colombini, Tatsuo Nishitani, and Giovanni Taglialatela
Solvability and Nonsolvability of Second-Order Evolution Equations - Ferruccio Colombini, Ludovico Pernazza, and Francois Treves
Navier-Stokes Equations with Variable Density - Raphael Danchin
Recent III - Posedness Results for the Wave Map System in Critical Spaces - Piero D'Ancona and Vladimir Georgiev
Some Results on the Cauchy Problem for Hyperbolic Operators with Non-regular Coefficients - Daniele Del Santo
The Question of Solvability - Nils Dencker
Singularities of Solutions of Schrodinger Equations for Perturbed Harmonic Oscillators - Shin-ichi Doi
Dispersive Estimates for Principally Normal Operators and Applications to Unique Continuation - Herbert Koch and Daniel Tataru
On the Small Data Global Existence and Scattering for Systems of Semilinear Wave Equations - Hideo Kubo
Well Posedness of 2 x 2 Systems with C Infinity-Coefficients - Lorenzo Mencherini and Sergio Spagnolo
Large Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems - Guy Metivier and Kevin Zumbrun
Scalar Local Covariant Fields on a Family of Globally Hyperbolic Manifolds – M.K. Venkatesha Murthy
On Lower Bounds of Pseudodifferential Systems - Alberto Parmeggiani
A Refined Diagonalization Procedure to Handle Fast Oscillations in Degenerate Hyperbolic Problems - Michael Reissig
Analytic Theory for the Quadratic Scattering, Wave Front Set and Application to the Schrodinger Equation - Luc Robbiano and Claude Zuily
On Some Stability Theorem of the Steady Flow of Compressible Viscous Fluid with Respect to the Initial Disturbance - Yoshihiro Shibata
Initial Boundary Value Problem for the Equations of Ideal Magnetohydrodynamics in a Half Space - Masahiro Takayama
Differential Algebra and Completely Integrable Systems - Francois Treves
Diagonalizable Complex Systems, Reduced Dimension and Hermitian Systems I - Jean Vaillant
The Cauchy Problem for Hyperbolic Operators Dominated by Time Functions - Seiichiro Wakabayashi