Singularities in Boundary Value Problems : Proceedings of the NATO Advanced Study Institute held at Maratea, Italy, September 22October 3, 1980
 Responsibility
 edited by H.G. Garnir.
 Imprint
 Dordrecht : Springer Netherlands, 1981.
 Physical description
 1 online resource (400 pages)
 Series
 NATO advanced study institutes series. Series C, Mathematical and physical sciences ; 65.
Online
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Description
Creators/Contributors
 Author/Creator
 Garnir, H. G.
Contents/Summary
 Contents

 Sur le Comportement Semi Classique du Spectre et de l'Amplitude de Diffusion d'un Hamiltonien Quantique
 General InitialBoundary Problems for Second Order Hyperbolic Equations
 Note on a Singular InitialBoundary Value Problem
 PseudoDifferential Operators of Principal Type
 Mixed Problems for the Wave Equation
 Microlocal Analysis of Boundary Value Problems with Applications to Diffraction
 Transformation Methods for Boundary Value Problems
 Propagation of Singularities and the Scattering Matrix
 Propagation at the Boundary of Analytic Singularities
 Lower Bounds at Infinity for Solutions of Differential Equations with Constant Coefficients in Unbounded Domains
 Analytic Singularities of Solutions of Boundary Value Problems
 Diffraction Effects in the Scattering of Waves
 Singularities of Elementary Solutions of Hyperbolic Equations with Constant Coefficients
 The Mixed Problem for Hyperbolic Systems.
 Summary
 The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves,  The!'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudodifferential operators, Fourier integral operators, microfunctions,  ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.
Subjects
Bibliographic information
 Publication date
 1981
 Title variation
 Proceedings of the NATO Advanced Study Institute, Maratea, Italy, September 22October 3, 1980
 Series
 NATO Advanced Study Institutes Series, Series CMathematical and Physical Sciences, 13892185 ; 65
 ISBN
 9789400984349 (electronic bk.)
 9400984340 (electronic bk.)
 9789400984363 (print)
 9400984367 (print)
 DOI
 10.1007/9789400984349