Regularity of elastic waves in the glancing region of \(P\) waves
type: Item
instance of: scholarly article
title: Regularity of elastic waves in the glancing region of \(P\) waves
zbMATH Open document ID: 1054.58503
author: Tatsushi Morioka
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2001-02-20T00:00:00Z
review text: The author studies the isotropic elastic equation with Dirichlet condition at the boundary. The domain \(\Omega\subset\mathbb R^3\) is exterior, \(\partial\Omega\) is analytic and \(\mathbb R^3\subset\Omega\) is strictly convex, i.e. the Gaussian curvature of \(\partial\Omega\) is positive everywhere. Then it is proved that the outgoing solutions of the problem under consideration have the Gevrey \(G_3\) regularity in the glancing region of the longitudinal waves. The proof of the main theorem of this paper relies on some investigations of Lebeau for the wave equation and on the investigation of P. D. Stefanov and G. Vodev [Duke Math. J. 78, No. 3, 677--714 (1995; Zbl 0846.35139)] for the Neumann problem in linear elasticity outside a strictly convex body.
Mathematics Subject Classification ID: 58J47
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74H30
Mathematics Subject Classification ID: 74J05
zbMATH DE Number: 1437023
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143495
OpenAlex ID: W2038572003
DOI: 10.2977/PRIMS/1195143495
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description: scientific article; zbMATH DE number 1437023