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• W3111370206 abstract "<p style='text-indent:20px;'>We investigate a multidimensional transmission problem between viscoelastic system with localized Kelvin-Voigt damping and purely elastic system under different types of geometric conditions. The Kelvin-Voigt damping is localized via non smooth coefficient in a suitable subdomain. It was shown that the discontinuity of the material coefficient along the interface elastic/viscoelastic can't assure an exponential stability of the total system. So, it is natural to hope for a polynomial stability result under certain geometric conditions on the damping region. For this aim, using frequency domain approach combined with a new multiplier technic, we will establish a polynomial energy decay estimate of type <inline-formula><tex-math id=M1>begin{document}$ t^{-1} $end{document}</tex-math></inline-formula> for smooth initial data. This result is obtained if either one of the geometric assumptions (A1) or (A2) holds (see below). Also, we establish a general polynomial energy decay estimate on a bounded domain where the geometric conditions on the localized viscoelastic damping are violated and we apply it on a square domain where the damping is localized in a vertical strip. However, the energy of our system decays polynomially of type <inline-formula><tex-math id=M2>begin{document}$ t^{-2/5} $end{document}</tex-math></inline-formula> if the strip is localized near the boundary. Else, it's of type <inline-formula><tex-math id=M3>begin{document}$ t^{-1/3} $end{document}</tex-math></inline-formula>. The main novelty in this paper is that the geometric situations covered here are richer and less restrictive than those considered in [<xref ref-type=bibr rid=b31>31</xref>], [<xref ref-type=bibr rid=b28>28</xref>], [<xref ref-type=bibr rid=b19>19</xref>] and include in particular an example where the damping region is localized faraway from the boundary. Note that part of the results of this paper was announced in [<xref ref-type=bibr rid=b22>22</xref>].</p>" @default.
• W3111370206 created "2020-12-21" @default.
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• W3111370206 date "2021-01-01" @default.
• W3111370206 modified "2023-09-28" @default.
• W3111370206 title "Stability of N-D transmission problem in viscoelasticity with localized Kelvin-Voigt damping under different types of geometric conditions" @default.
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• W3111370206 doi "https://doi.org/10.3934/mcrf.2020050" @default.
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