Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

Luc Robbiano and Qiong Zhang
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Luc Robbiano: Laboratoire de Mathématiques Appliquées, UMR 8100 du CNRS, Université Paris–Saclay (site UVSQ), 45 avenue des Etats Unis, 78035 Versailles, France
Qiong Zhang: School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2020, vol. 8, issue 5, 1-19

Abstract: In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator. As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on which the damping is effective.

Keywords: Carleman estimate; wave equation; Kelvin-Voigt damping; logarithmic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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