loading page

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
Author Profile
Mama Abdelli
University of Djillali Liabes Sidi Bel Abbes
Author Profile
Abderrahmane Beniani
Center University of Belhadj Bouchaib -B.P. 284 RP, Ain Temouchent
Author Profile

Abstract

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 \(p\geq\max\{l+2,m\}\).