Hyperbolic Equations and Related Topics

Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.

Preface

Comments on the Development of Hyperbolic Analysis

Complex Vector Fields, Holomorphic Extension of CR Functions and Related Problems

Second Microlocalization and Propagation of Singularities for Semi-Linear Hyperbolic Equations

Le Domaine d'Existence et le Prolongement Analytique des Solutions des Problemes de Goursat et de Cauchy a Donnees Singulieres

On the Scattering Matrix for Two Convex Obstacles

Three Spectral Problems Revised

The Cauchy Problem for Effectively Hyperbolic Equations

The Cauchy Problem for Uniformly Diagonalizable Hyperbolic Systems in Gevrey Classes

Quasi-Positivity for Pseudodifferential Operators and Microlocal Energy Methods

Systems of Microdifferential Equations of Infinite Order

Irregularity of Hyperbolic Operators

Propagation for the Wave Group of a Positive Subelliptic Second-Order Differential Operator

On the Cauchy Problem for Hyperbolic Equations and Related Problems —Micro-local Energy Method

Microlocal Energy Estimates for Hyperbolic Operators with Double Characteristics

Huygens' Principle for a Wave Equation and the Asymptotic Behavior of Solutions along Geodesies

Le Probleme de Cauchy a Caracteristiques Multiples dans la Classe de Gevrey -Coefficients Holderiens en t-

Solutions with Singularities on a Surface of Linear Partial Differential Equations

Poisson Relation for Manifolds with Boundary

Mixed Problems for Evolution Operators with Dominant Principal Parts in the Volevich-Gindikin Sense

Tunnel Effects for Semiclassical Schrodinger Operators

Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time

Fundamental Solution for the Cauchy Problem of Hyperbolic Equation in Gevrey Class and the Propagation of Wave Front Sets

Ramifications d'Integrales Holomorphes

Generalized Hamilton Flows and Singularities of Solutions of the Hyperbolic Cauchy Problem