Global nonexistence of arbitrary initial energy solutions of viscoelastic equation with nonlocal boundary damping
type: Item
instance of: scholarly article
title: Global nonexistence of arbitrary initial energy solutions of viscoelastic equation with nonlocal boundary damping
zbMATH Open document ID: 1282.35094
author: Jie Ma
author: Hongrui Geng
published in: Taiwanese Journal of Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/2742
review text: The main goal of this paper is to investigate the blowing-up solutions to the initial value problem for the viscoelastic wave equation \[ u_{tt} - \Delta u + \int^t_0g(t - \tau)\text{div}(a(x)\nabla u(x,\tau))d\tau + u_t = 0\quad\text{in}\;\Omega \times (0,\infty) \] under boundary damping. The aim is to give a sufficient condition on the initial datum under which the solution blows up in finite time. The method of the proof is based on the concavity argument.
reviewed by: Daniel Ševčovič
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 6137987
zbMATH Keywords: concavity argument
MaRDI profile type: Publication
OpenAlex ID: W4245757460
DOI: 10.11650/TWJM/1500406836
description: scientific article; zbMATH DE number 6137987