Research Communication | Open Access
Volume 2020 | Communication ID 8 |

Existence and energy decay of solutions for a nonlinear wave equation with a constant weak delay and a logarithmic nonlinearity

Melouka Remil
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
19 September 2019
04 October 2019
10 March 2020

Abstract: In this work, we consider a nonlinear viscoelastic wave equation with a weak internal constant delay term and a logarithmic nonlinearity: \begin{equation*} u_{tt}(x,t)-\Delta u(x,t)-\Delta u_{tt}(x,t)+\mu_{1}(t)u_{t}(x,t)+ \mu_{2}(t)u_{t}(x,t-\tau)=u \ln|u|^{k}. \end{equation*} In a bounded domain. Under appropriate conditions on $\mu_1$ and $\mu_2$, we prove global existence of solutions by the Faedo–Galerkin method and establish a decay rate estimate for the energy using the multiplier method.