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

Abstract

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