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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {Logarithmic stabilization of the {Kirchhoff} plate transmission system with locally distributed {Kelvin-Voigt} damping},
     journal = {Applications of Mathematics},
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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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