Global existence and blowup of solutions for a class of nonlinear higher-order wave equations
type: Item
instance of: scholarly article
title: Global existence and blowup of solutions for a class of nonlinear higher-order wave equations
zbMATH Open document ID: 1262.35172
author: Jun Zhou
author: Xiaojun Song
author: Xiongrui Wang
author: Chunlai Mu
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2012-07-31T00:00:00Z
review text: The authors considered a class of nonlinear higher-order wave equation with nonlinear damping \(u_{tt}+(-\Delta)^m u+a|u_t|^{p-2}u_t=b|u|^{q-2}u\) in a bounded domain \(\Omega\subset\mathbb{R}^N\) (\(m, N \geq 1\) are natural numbers, \(a,b>0\) and \(p,q>2\)), with boundary conditions \(D^\alpha u(x,t)=0\) for \(|\alpha|\leq m-1\). They showed that the solution is global in time under some conditions without the relation between \(p\) and \(q\), and they also showed that the local solution blows up in finite time if \(q > p\) with some assumptions on the initial energy. The decay estimate of the energy function for the global solution and the lifespan for the blow-up solution are also given. This extends the recent results of \textit{Y. Ye} [J. Inequal. Appl. 2010, Article ID 394859, 14 p. (2010; Zbl 1190.35161)].
Mathematics Subject Classification ID: 35L76
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6062091
zbMATH Keywords: energy decay
zbMATH Keywords: lifespan
zbMATH Keywords: nonlinear damping
reviewed by: Chengbo Wang
MaRDI profile type: Publication
full work available at URL: s00033-011-0165-9
OpenAlex ID: W2017362217
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DOI: 10.1007/S00033-011-0165-9
description: scientific article; zbMATH DE number 6062091