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Blow-up of result in a nonlinear wave equation with delay and source term
  • Tayeb Lakroumbe,
  • Mama Abdelli,
  • Abderrahmane Beniani
Tayeb Lakroumbe
University of Djillali Liabes Faculty of Exact Sciences
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Mama Abdelli
University of Djillali Liabes Sidi Bel Abbes
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Abderrahmane Beniani
Center University of Belhadj Bouchaib -B.P. 284 RP, Ain Temouchent
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In this paper we consider the initial boundary value problem for a nonlinear damping and a delay term of the form:

\begin{equation} |u_{t}|^{l}u_{tt}-\Delta u(x,t)-\Delta u_{tt}+\mu_{1}|u_{t}|^{m-2}u_{t}\\ +\mu_{2}|u_{t}(t-\tau)|^{m-2}u_{t}(t-\tau)=b|u|^{p-2}u,\nonumber \\ \end{equation}

with initial conditions and Dirichlet boundary conditions. Under appropriate conditions on \(\mu_{1},\,\ \mu_{2}\), we prove that there are solutions with negative initial energy that blow-up finite time if \(p\geq\max\{l+2,m\}\).