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Optimal polynomial stability of a string with locally distributed Kelvin–Voigt damping and nonsmooth coefficient at the interface
Author(s) -
Ghader Mouhammad,
Nasser Rayan,
Wehbe Ali
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6918
Subject(s) - mathematics , bounded function , viscoelasticity , mathematical analysis , multiplier (economics) , polynomial , work (physics) , stability (learning theory) , domain (mathematical analysis) , physics , quantum mechanics , thermodynamics , machine learning , computer science , economics , macroeconomics
The purpose of this paper is to investigate the stabilization of one‐dimensional wave equation with localized internal viscoelastic damping of Kelvin–Voigt type in a bounded domain. In this work, we consider only one damping Kelvin–Voigt mechanism acting in the internal of the body. Using frequency domain arguments combined with the multiplier method, we prove that the energy of the system has the optimal decay of type t −4 .