Blow up for nonlinear dissipative wave equations in \(\mathbb R^n\)
type: Item
instance of: scholarly article
title: Blow up for nonlinear dissipative wave equations in \(\mathbb R^n\)
zbMATH Open document ID: 1065.35200
author: Grozdena Todorova
author: Enzo Vitillaro
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: This paper deals with the Cauchy problem for the following semilinear hyperbolic equation: \[ u_{tt}-\Delta u+|u_t|^{m-1}u_t=|u|^{p-1}u, \] with \(1\leq m<p\), \(p<\frac n{n-2}\), \(n\geq 3\). It is proved that for each \(\alpha>0\), \(\lambda\geq 0\) one can find infinitely many compactly supported initial data \(u_0, u_1\) having appropriately defined energy \(E=\lambda\) and \(\|\nabla u_0\|_2=\alpha\) but the solution \(u\) of the above mentioned Cauchy problem blows up in finite time.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2141753
zbMATH Keywords: semilinear hyperbolic equation
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.039
OpenAlex ID: W1971172800
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DOI: 10.1016/J.JMAA.2004.08.039
description: scientific article; zbMATH DE number 2141753