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

Abstract: The purpose of this paper is to investigate the stabilization of a one-dimensional 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 combining with a multiplier method, we prove a polynomial energy decay rate of order 1/t.