### Electronic Research Archive

2020, Issue 1: 205-220. doi: 10.3934/era.2020014

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

• Received: 01 January 2020 Revised: 01 February 2020
• Primary: 35D05, 35E15; Secondary: 35Q35

• We consider the wave equation with a weak internal damping with non-constant delay and nonlinear weights given by

$\begin{eqnarray*} \label{NLS} u_{tt}(x,t) - u_{xx}(x,t)+\mu_1(t)u_t(x,t) +\mu_2(t)u_t(x,t-\tau(t)) = 0 \end{eqnarray*}$

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.

Citation: Vanessa Barros, Carlos Nonato, Carlos Raposo. Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights[J]. Electronic Research Archive, 2020, 28(1): 205-220. doi: 10.3934/era.2020014

### Related Papers:

• We consider the wave equation with a weak internal damping with non-constant delay and nonlinear weights given by

$\begin{eqnarray*} \label{NLS} u_{tt}(x,t) - u_{xx}(x,t)+\mu_1(t)u_t(x,t) +\mu_2(t)u_t(x,t-\tau(t)) = 0 \end{eqnarray*}$

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.

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