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Zbl 0803.35092
Existence of a solution of the wave equation with nonlinear damping and source terms.
(English)
[J] J. Differ. Equations 109, No.2, 295-308 (1994). ISSN 0022-0396

The authors study the problem of nonlinear wave equation $u\sb{tt} - \Delta u + au\sb t \vert u\sb t \vert\sp{m-1} = bu \vert u \vert\sp{p-1}$ in $\Omega \subseteq\bbfR\sp n$ with Dirichlet boundary conditions on $\partial \Omega$, where $p>1$ for $n \le 2$, $1 \le p \le {n \over n - 2}$ for $n \ge 3$ and $a,b>0$. They prove a global existence of the solution to the above problem for large initial data and $1,p \le m$ and blowing-up of $L\sb \infty$-norm of solution for suitably large initial data and $1<m<p$.
[M.Kopáčková (Praha)]
MSC 2000:
*35L70 Second order nonlinear hyperbolic equations
35L20 Second order hyperbolic equations, boundary value problems

Keywords: blow-up solution; energy inequality; nonlinear wave equation; global existence

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