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Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms

Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms

Authors :
Hongwei Zhang
Qingying Hu
Source :
Electronic Journal of Differential Equations, Vol 2007, Iss 76, Pp 1-10 (2007)
Publication Year :
2007
Publisher :
Texas State University, 2007.

Abstract

This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation $$ u_{tt}-Delta u +|u|^kj'(u_t)=|u|^{p-1}u quad hbox{in }Omega imes (0,T), $$ where $p>1$ and $j'$ denotes the derivative of a $C^1$ convex and real value function $j$. We prove that every weak solution is asymptotically stability, for every $m$ such that $0k+m$ and the initial data is positive, but appropriately bounded.

Details

Language :
English
ISSN :
10726691
Volume :
2007
Issue :
76
Database :
Directory of Open Access Journals
Journal :
Electronic Journal of Differential Equations
Publication Type :
Academic Journal
Accession number :
edsdoj.ba3ca1dcc5574878a19cd5cf44e50504
Document Type :
article