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Zbl 0990.35102
Messaoudi, Salim A.
Blow up in a nonlinearly damped wave equation.
(English)
[J] Math. Nachr. 231, 105-111 (2001). ISSN 0025-584X; ISSN 1522-2616/e

Author's abstract: We consider the nonlinearly damped semilinear wave equation $$u_{tt}-\triangle u+au_{t}|u_{t}|^{m-2}=bu|u|^{p-2}$$ associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative energy, blows up in finite time if $p>m.$ This result improves an earlier one in the paper of {\it V. Georgiev} and {\it G. Todorova} [J. Differ. Equ. 109, 295-308 (1994; Zbl 0803.35092)].
[Marie Kopáčková (Praha)]
MSC 2000:
*35L70 Second order nonlinear hyperbolic equations
35L20 Second order hyperbolic equations, boundary value problems
35B40 Asymptotic behavior of solutions of PDE

Keywords: semilinear wave equation; energy estimate; Dirichlet boundary conditions

Citations: Zbl 0803.35092

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