Blow up in a nonlinearly damped wave equation

Authors
Messaoudi, SA
Citation
Sa. Messaoudi, Blow up in a nonlinearly damped wave equation, MATH NACHR, 231, 2001, pp. 105-111
Citations number
10
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
231
Year of publication
2001
Pages
105 - 111
Database
ISI
SICI code
0025-584X(2001)231:<105:BUIAND>2.0.ZU;2-3
Abstract
In this paper we consider the nonlinearly damped semilinear wave equation u(tt) - Deltau + au(t)\u(t)\ (m-2) = bu \u \ (p-2) associated with initial and Dirichlet boundary conditions. We prove that an y strong solution, with negative initial energy, blows up in finite time if p>m. This result improves an earlier one in [2].