Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay

<p style='text-indent:20px;'>The purpose of this paper is to investigate the stabilization a locally coupled wave equations with non smooth localized viscoelastic damping Kelvin-Voigt type and time delay. Using general criteria Arendt-Batty, we show strong stability our system in absence compactness resolvent. Finally, using frequency domain approach combined multiplier method, prove polynomial energy decay rate order <inline-formula><tex-math id="M1">\begin{document}$ t^{-1} $\end{document}</tex-math></inline-formula>.</p>