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Logarithmic Decay of a Wave Equation with Kelvin-Voigt Damping

Abstract

In this paper we analyze the long time behavior of a wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-differential 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.
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Dates and versions

hal-01866131 , version 1 (06-09-2018)

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Luc Robbiano, Qiong Zhang. Logarithmic Decay of a Wave Equation with Kelvin-Voigt Damping. 2018. ⟨hal-01866131⟩
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