Hyperbolic Equations and Related Topics

Hyperbolic Equations and Related Topics

Proceedings of the Taniguchi International Symposium, Katata and Kyoto, 1984

1st Edition - April 8, 1987

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  • Editor: Sigeru Mizohata
  • eBook ISBN: 9781483269252

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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.

Table of Contents

  • 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

Product details

  • No. of pages: 458
  • Language: English
  • Copyright: © Academic Press 1987
  • Published: April 8, 1987
  • Imprint: Academic Press
  • eBook ISBN: 9781483269252

About the Editor

Sigeru Mizohata

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