On the exponential decay of the energy of a linear thermoelastic plate
type: Item
instance of: scholarly article
title: On the exponential decay of the energy of a linear thermoelastic plate
zbMATH Open document ID: 0811.73006
author: Yoshihiro Shibata
published in: Computational and Applied Mathematics
publication date: 1995-05-07T00:00:00Z
review text: The linear plate equations in a bounded domain in \(\mathbb{R}^ n\), \(u_{tt} + \Delta^ 2 u + \alpha \Delta \theta = 0\), \(\theta_ t - \beta \Delta \theta - \alpha \Delta u_ t = 0\), \(\beta, | \alpha| > 0\), are studied with prescribed initial conditions and with the following Neumann type boundary conditions: the function \(v = \Delta u + \alpha \theta\) as well as the normal derivatives of \(v\) and of \(\theta\) vanish on the boundary. For this mathematically interesting problem it is shown the well-posedness along with semigroup theory, and the exponential decay using energy methods.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 704198
zbMATH Keywords: biharmonic operator
zbMATH Keywords: Neumann type boundary conditions
zbMATH Keywords: well-posedness
zbMATH Keywords: semigroup theory
reviewed by: Reinhard Racke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 704198