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The 1985 Castel vecchio-Pas coli NATO Advanced Study Institute is aimed to complete the trilogy with the two former institutes I organized : "Boundary Value Problem for Evolution Partial Differential Operators", Liege, 1976 and "Singularities in Boundary Value Problems", Maratea, 1980. It was indeed necessary to record the considerable progress realized in the field of the propagation of singularities of Schwartz Distri butions which led recently to the birth of a new branch of Mathema tical Analysis called Microlocal Analysis. Most of this theory was mainly built to be applied to distribution solutions of linear partial differential problems. A large part of this institute still went in this direction. But, on the other hand, it was also time to explore the new trend to use microlocal analysis In non linear differential problems. I hope that the Castelvecchio NATO ASI reached its purposes with the help of the more famous authorities in the field. The meeting was held in Tuscany (Italy) at Castelvecchio-Pascoli, little village in the mountains north of Lucca on September 2-12, 1985. It was hosted by "11 Ciocco" an international vacation Center, In a comfortable hotel located in magnificent mountain surroundings and provided with all conference and sport facilities.
Sommario
Convergence of Formal Solutions of Singular Partial Differential Equations.- Singularitiés des Solutions de Problèmes de Cauchy Hyperboliques Non Linéaires.- Fourier Integral Operators of Infinite Order on Gevrey Spaces. Applications to the Cauchy Problem for Hyperbolic Operators.- Singularities, Supports and Lacunas.- On the Wave Equation in Plane Regions with Polygonal Boundary.- The Necessity of the Irregularity Condition for Solvability in Gevrey Classes (s) and {s}.- Asymptotic Solutions of Hyperbolic Boundary Value Problems with Diffraction.- Propagation des Singularités Gevrey pour le Problème de Dirichlet.- Conormal Rings and Semilinear Wave Equations.- General Boundary Value Problems in the Framework of Hyperfunctions.- Study of Sheaves of Solutions of Microdifferential Systems.- Effet Tunnel pour l'Opérateur de Schrödinger Semi-Classique.- Propagation of Singularities for Hamilton-Jacobi Equation.- Ramifications of Holomorphic Integrals.- Generalized Flows and Their Applications.
