Blow-up and global existence analysis for the viscoelastic wave equation with a frictional and a Kelvin-Voigt damping
type: Item
instance of: scholarly article
title: Blow-up and global existence analysis for the viscoelastic wave equation with a frictional and a Kelvin-Voigt damping
zbMATH Open document ID: 1440.35215
DOI: 10.1155/2018/8931856
author: Fosheng Wang
author: Chengqiang Wang
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously. By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is ``weaker,'' in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 6992036
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8931856
OpenAlex ID: W2800678287
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Wikidata QID: Q129894631
description: scientific article; zbMATH DE number 6992036