Hyperbolic Equations and Related Topics

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

Sigeru Mizohata

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780125016582
• eBook ISBN: 9781483269252
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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

• Front Cover
• Hyperbolic Equations and Related Topics
• Copyright Page
• Table of Contents
• Preface
• Comments on the Development of Hyperbolic Analysis
• Chapter 1. Complex Vector Fields, Holomorphic Extension of CR Functions and Related Problems
• Chapter 2. Second Microlocalization and Propagation of Singularities for Semi-Linear Hyperbolic Equations
• Chapter 3. Le Domaine d'Existence et le Prolongement Analytique des Solutions des Problèmes de Goursat et de Cauchy à Données Singulières
• Chapter 4. On the Scattering Matrix for Two Convex Obstacles
• Chapter 5. Three Spectral Problems Revised
• Chapter 6. The Cauchy Problem for Effectively Hyperbolic Equations (Remarks)
• Chapter 7. The Cauchy Problem for Uniformly Diagonalizable Hyperbolic Systems in Gevrey Classes
• Chapter 8. Quasi-Positivity for Pseudodifferential Operators and Microlocal Energy Methods
• Chapter 9. Systems of Microdifferential Equations of Infinite Order
• Chapter 10. Irregularity of Hyperbolic Operators
• Chapter 11. Propagation for the Wave Group of a Positive Subelliptic Second-Order Differential Operator
• Chapter 12. On the Cauchy Problem for Hyperbolic Equations and Related Problems: Micro-local Energy Method
• Chapter 13. Microlocal Energy Estimates for Hyperbolic Operators with Double Characteristics
• Chapter 14. Huygens' Principle for a Wave Equation and the Asymptotic Behavior of Solutions along Geodesics
• Chapter 15. Le Problème de Cauchy à Caractéristiques Multiples dans la Classe de Gevrey: coefficients hölderiens en t
• Chapter 16. Solutions with Singularities on a Surface of Linear Partial Differential Equations
• Chapter 17. Poisson Relation for Manifolds with Boundary
• Chapter 18. Mixed Problems for Evolution Operators with Dominant Principal Parts in the Volevich-Gindikin Sense
• Chapter 19. Tunnel Effects for Semiclassical Schrödinger Operators
• Chapter 20. Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time
• Chapter 21. Fundamental Solution for the Cauchy Problem of Hyperbolic Equation in Gevrey Class and the Propagation of Wave Front Sets
• Chapter 22. Remification d'intégrates holomorphes
• Chapter 23. Generalized Hamilton Flows and Singularities of Solutions of the Hyperbolic Cauchy Problem