Diffraction by a convex obstacle
type: Item
instance of: scholarly article
title: Diffraction by a convex obstacle
zbMATH Open document ID: 0831.35121
DOI: 10.1007/BF01231531
author: T. Hargé
author: Gilles Lebeau
published in: Inventiones Mathematicae
publication date: 1995-01-29T00:00:00Z
full work available at URL: https://eudml.org/doc/144234
review text: The purpose of the present paper is to derive results regarding the diffraction of waves by an obstacle in adapting a method already used by the first author in the study of the heat equation. It has been conjectured that the decay rate in the shadow area should be in the form \(\exp (- C \omega^{1/3})\) where \(C\) is a constant related to the geometry of the geodesic flow on the boundary of the obstacle. This result has been already proven for analytic boundaries, and here one considers the case of an obstacle with \(C^\infty\) boundary. The main strategy to establish the basic theorem is the following. (i) The so- called Airy's inequality, (ii) the estimation of the velocity of propagation on the solving kernels, and (iii) the use of complex deformation on the normal variables on the boundary.
reviewed by: Guy Jumarie
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 703881
zbMATH Keywords: obstacle with \(C^ \infty\) boundary
zbMATH Keywords: diffraction of waves by an obstacle
zbMATH Keywords: decay rate in the shadow area
MaRDI profile type: Publication
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cites work: Q3792014
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OpenAlex ID: W2060119145
description: scientific article; zbMATH DE number 703881