Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights

Abstract

We consider the wave equation with a weak internal damping with non-constant delay and nonlinear weights given by \begin{document}$ \begin{eqnarray*} \label{NLS} u_{tt}(x,t) - u_{xx}(x,t)+\mu_1(t)u_t(x,t) +\mu_2(t)u_t(x,t-\tau(t)) = 0 \end{eqnarray*} $\end{document} in a bounded domain. Under proper conditions on nonlinear weights $ \mu_1(t), \mu_2(t) $ and non-constant delay $ \tau(t) $, we prove global existence and estimative the decay rate for the energy.

Topics & Concepts