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Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 733--741 | DOI:10.5890/DNC.2021.12.012

Tayeb Lakroumbe, Mama Abdelli, Abderrahmane Beniani

Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, P. O. Box 89, Sidi Bel Abbes 22000, Algeria University of Mascara, 29000, Algeria University Center of Ain Temouchent, Department of Mathematics, Ain Temouchent 46000, Algeria

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Abstract

In this paper we consider the initial boundary value problem for a nonlinear damping and a delay term of the form: $$ |u_t|^{l}u_{tt}-\Delta u (x,t) -\Delta u_{tt}+\mu_1|u_t|^{m-2}u_t\\+\mu_2|u_t(t-\tau)|^{m-2}u_t(t-\tau)=b|u|^{p-2}u, $$ 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 $p \geq \max\{l+2,m\}$.

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