Geodesic
Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping
Applications of Mathematics, Tome 67 (2022) no. 1, pp. 21-47

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We are concerned with a transmission problem for the Kirchhoff plate equation where one small part of the domain is made of a viscoelastic material with the Kelvin-Voigt constitutive relation. We obtain the logarithmic stabilization result (explicit energy decay rate), as well as the wellposedness, for the transmission system. The method is based on a new Carleman estimate to obtain information on the resolvent for high frequency. The main ingredient of the proof is some careful analysis for the Kirchhoff transmission plate equation.
DOI : 10.21136/AM.2021.0104-20
Classification : 35L57, 35Q74, 74K20, 74M05, 93D15
Keywords: transmission problem; Kirchhoff plate; Kelvin-Voigt damping; energy decay; Carleman estimate 
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Hong, Gimyong; Hong, Hakho. Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping. Applications of Mathematics, Tome 67 (2022) no. 1, pp. 21-47. doi: 10.21136/AM.2021.0104-20

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