Open AccessStability 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 and 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 , stability (learning theory) , multiplier (economics) , mathematical analysis , mathematics , physics , wave equation , polynomial , exponential stability , quantum mechanics , computer science , thermodynamics , nonlinear system , macroeconomics , machine learning , economics
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} .