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

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  • 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 $ t^{-1} $.

    Mathematics Subject Classification: Primary: 93C43, 93D15, 93D20; Secondary: 35L05, 93C80.


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  • Figure 1.  Local Kelvin-Voigt damping and local time delay feedback

    Figure 2.  Geometric description of the functions $ \chi_1 $ and $ \chi_2 $

    Figure 3.  Geometric description of the functions $ \theta_1 $, $ \theta_2 $ and $ \theta_3 $

    Figure 4.  Geometric description of the functions $ \theta_4 $ and $ \theta_5 $

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