On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary
type: Item
instance of: scholarly article
title: On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary
zbMATH Open document ID: 1072.35114
author: Jeong Ja Bae
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-05-12T00:00:00Z
review text: The author considers in \(Q=(0,\infty)\times \Omega, \)where \(\Omega\) can be non-simple-connected, a mixed problem for a system of two coupled Kirchhoff type equations of second order. The boundary of \(\Omega\) is divided in two parts \(\Gamma_0\) and \(\Gamma_1\). On \(\Gamma_0\) the condition \[ u=v=\frac{\partial u}{\partial \nu}=\frac{\partial v}{\partial \nu}=0 \tag{1} \] is posed and on \(\Gamma_1\) a condition with a memory effect. The author claims the existence of global solutions and uniform decay of the energy. Condition (1) looks like exessive because if \(\Gamma_1\) is empty, then one has Cauchy data for the Laplace equation on \(\Gamma_0\). In this case, the problem is overdetermined.
Mathematics Subject Classification ID: 35L55
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 2167864
zbMATH Keywords: Kirchhoff equation
zbMATH Keywords: stability
zbMATH Keywords: decay of the energy
MaRDI profile type: Publication
full work available at URL: j.na.2004.11.014
OpenAlex ID: W2059363774
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DOI: 10.1016/J.NA.2004.11.014
description: scientific article; zbMATH DE number 2167864