Discontinuity, Nonlinearity, and Complexity
Blowup of Result in a Nonlinear Wave Equation with Delay and Source Term
Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 733741  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:
$$
u_t^{l}u_{tt}\Delta u (x,t) \Delta u_{tt}+\mu_1u_t^{m2}u_t\\+\mu_2u_t(t\tau)^{m2}u_t(t\tau)=bu^{p2}u,
$$
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 blowup finite time if $p \geq \max\{l+2,m\}$.
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