Decay of solutions for a viscoelastic wave equation with acoustic
boundary conditions
Abstract
In this report we prove that the hypothesis on the memory term $g$ in
\cite% {WenjunYunSun} can be modified to be
$g^{\prime }(t)\leq
-\zeta (t)g^{p}(t)$% , $t\geq 0,$
$1\leq p<\frac{3}{2}$
where $\zeta (t)$ provides%
\begin{equation*} \zeta
\left( 0\right)
>0,\text{ }\zeta
^{\prime }(t)\leq
0,\text{ }%
\int_{0}^{\infty
}\zeta \left( s\right)
ds=+\infty . \end{equation*}% So the
optimal decay results are extended.