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

@article{Akil2020StabilityRO,
  title={Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay},
  author={Mohammad Akil and Haidar Badawi and Ali Wehbe},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
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. 
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