Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping

Gimyong Hong; Hakho Hong

Applications of Mathematics (2022)

  • Volume: 67, Issue: 1, page 21-47
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hong, Gimyong, and Hong, Hakho. "Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping." Applications of Mathematics 67.1 (2022): 21-47. <http://eudml.org/doc/298253>.

@article{Hong2022,
abstract = {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.},
author = {Hong, Gimyong, Hong, Hakho},
journal = {Applications of Mathematics},
keywords = {transmission problem; Kirchhoff plate; Kelvin-Voigt damping; energy decay; Carleman estimate},
language = {eng},
number = {1},
pages = {21-47},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping},
url = {http://eudml.org/doc/298253},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Hong, Gimyong
AU - Hong, Hakho
TI - Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 21
EP - 47
AB - 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.
LA - eng
KW - transmission problem; Kirchhoff plate; Kelvin-Voigt damping; energy decay; Carleman estimate
UR - http://eudml.org/doc/298253
ER -

References

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