Hyperbolic Equations and Related Topics : Proceedings of the Taniguchi International Symposium, Katata and Kyoto, 1984

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. Content: Front Matter, Page iii Copyright, Page iv Preface, Page v, S. Mizohata Comments on the Development of Hyperbolic Analysis, Pages ix-xxxiv, S. Mizohata, Y. Ohya, M. Ikawa Complex Vector Fields, Holomorphic Extension of CR Functions and Related Problems, Pages 1-9, M.S. BAOUENDI Second Microlocalization and Propagation of Singularities for Semi-Linear Hyperbolic Equations, Pages 11-49, Jean-Michel BONY Le Domaine d'Existence et le Prolongement Analytique des Solutions des Problèmes de Goursat et de Cauchy à Données Singulières, Pages 51-62, Yûsaku HAMADA, Akira TAKEUCHI On the Scattering Matrix for Two Convex Obstacles, Pages 63-84, Mitsuru IKAWA Three Spectral Problems Revised, Pages 85-88, Victor IVRI The Cauchy Problem for Effectively Hyperbolic Equations (Remarks), Pages 89-100, Nobuhisa IWASAKI The Cauchy Problem for Uniformly Diagonalizable Hyperbolic Systems in Gevrey Classes, Pages 101-123, Kunihiko KAJITANI Quasi-Positivity for Pseudodifferential Operators and Microlocal Energy Methods, Pages 125-141, Kiyômi KATAOKA Systems of Microdifferential Equations of Infinite Order, Pages 143-154, Takahiro KAWAI Irregularity of Hyperbolic Operators, Pages 155-179, Hikosaburo KOMATSU Propagation for the Wave Group of a Positive Subelliptic Second-Order Differential Operator, Pages 181-192, Richard MELROSE On the Cauchy Problem for Hyperbolic Equations and Related Problems: —Micro-local Energy Method—, Pages 193-233, Sigeru MIZOHATA Microlocal Energy Estimates for Hyperbolic Operators with Double Characteristics, Pages 235-255, Tatsuo NISHITANI Huygens' Principle for a Wave Equation and the Asymptotic Behavior of Solutions along Geodesies, Pages 257-271, Kimimasa NISHIWADA Le Problème de Cauchy à Caractéristiques Multiples dans la Classe de Gevrey: —coefficients hölderiens en t—, Pages 273-306, Yujiro OHYA, Shigeo TARAMA Solutions with Singularities on a Surface of Linear Partial Differential Equations, Pages 307-316, Sunao ŌUCHI Poisson Relation for Manifolds with Boundary, Pages 317-327, Vesselin M. PETKOV Mixed Problems for Evolution Operators with Dominant Principal Parts in the Volevich-Gindikin Sense, Pages 329-346, Reiko SAKAMOTO Tunnel Effects for Semiclassical Schrödinger Operators, Pages 347-362, J. SJÖSTRAND Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time, Pages 363-380, Sergio SPAGNOLO Fundamental Solution for the Cauchy Problem of Hyperbolic Equation in Gevrey Class and the Propagation of Wave Front Sets, Pages 381-394, Kazuo TANIGUCHI Remification d'intégrates holomorphes, Pages 395-414, Jean VAILLANT Generalized Hamilton Flows and Singularities of Solutions of the Hyperbolic Cauchy Problem, Pages 415-423, Seiichiro WAKABAYASHI