Decay of solutions of the elastic wave equation with a localized dissipation
type: Item
instance of: scholarly article
title: Decay of solutions of the elastic wave equation with a localized dissipation
zbMATH Open document ID: 1073.35036
author: Mourad Bellassoued
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2004-10-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73604
review text: The author studies two classical elastic wave equations: \(\partial_t^2 u-\Delta_e u=0\) and its damped version \(\partial_t^2 u-\Delta_e u+a(x)\partial_t u=0\) posed on a Riemannian manifold with a smooth and compact boundary and supplemented with damped and Dirichlet boundary conditions, respectively. Here, \(\Delta_e=\mu\Delta+(\mu+\lambda)\nabla ({div})\) where \(\mu>0\), \(2\mu+\lambda>0\), and \(\Delta\), \(\nabla\) and \(div\) are the Laplacian, gradient and the divergence operator associated to the Riemannian metric. For those initial-boundary value problem, the logarithmic decay in time of the energy functional is shown.
reviewed by: Grzegorz Karch
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 58J45
zbMATH DE Number: 2109722
zbMATH Keywords: elastic wave equation
zbMATH Keywords: decay of energy
zbMATH Keywords: Carleman estimates
zbMATH Keywords: Riemannian manifold
MaRDI profile type: Publication
OpenAlex ID: W2324966133
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DOI: 10.5802/AFST.1049
description: scientific article; zbMATH DE number 2109722