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