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

Mohammad Akil | Zendy; Haidar Badawi | Zendy; Ali Wehbe | Zendy

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

Author(s) -

Mohammad Akil,

Haidar Badawi,

Ali Wehbe

Publication year - 2021

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2021092

Subject(s) - viscoelasticity , resolvent , multiplier (economics) , stability (learning theory) , mathematics , mathematical analysis , polynomial , exponential stability , order (exchange) , wave equation , type (biology) , physics , pure mathematics , quantum mechanics , computer science , thermodynamics , nonlinear system , machine learning , economics , macroeconomics , ecology , finance , biology

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 \begin{document}$ t^{-1} $\end{document} .

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