The first mixed problem for the nonstationary Lamé system
type: Item
instance of: scholarly article
title: The first mixed problem for the nonstationary Lamé system
zbMATH Open document ID: 1396.35007
DOI: 10.1216/RMJ-2017-47-8-2731
author: O. I. Makhmudov
author: N. N. Tarkhanov
published in: Rocky Mountain Journal of Mathematics
publication date: 2018-02-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1517648609
review text: The authors study the initial-boundary value problem for the nonstationary Lamé system in elastodynamic \[ \begin{aligned} &\rho u_{tt}=-\mu \Delta u+(\lambda+\mu)\nabla \text{div}\,u+f,\;(x,t)\in \mathcal{X}\times (0,T),\\ & u(x,0)=u_0(x),\;u_t(x,0)=u_1(x),\;x\in \mathcal{X},\\& u(x,t)=0,\;(x,t)\in \partial\mathcal{X}\times (0,T), \end{aligned} \] where \(\mathcal{X}\subset \mathbb{R}^3 \) is a bounded domain with smooth boundary and \(u:\mathcal{X}\times (0,T)\to \mathbf{R}^3\) is a displacement vector. An existence and uniqueness result for weak solutions is stated using Fourier series and the Galerkin method applied also to classical hyperbolic problems. The regularity of the solution is verified too.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 6840998
zbMATH Keywords: Lamé system
zbMATH Keywords: initial-boundary value problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6840998