Longtime behavior of multidimensional wave equation with local Kelvin–Voigt damping

Zhong Jie Han; Kai Yu; Qiong Zhang

doi:10.1002/zamm.202000275

Longtime behavior of multidimensional wave equation with local Kelvin–Voigt damping

Zhong Jie Han^*, Kai Yu, Qiong Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, the longtime behavior of a coupled multidimensional elastic–viscoelastic waves system is considered. This model consists of an elastic wave domain and an viscoelastic wave domain, connecting by a common interface. The dissipative damping is produced in the viscoelastic wave via the boundary connection. By the resolvent estimate together with microlocal analysis argument, we show that the corresponding semigroup is polynomially stable with decay rate (Formula presented.) under certain conditions.

Original language	English
Article number	e202000275
Journal	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume	102
Issue number	6
DOIs	https://doi.org/10.1002/zamm.202000275
Publication status	Published - Jun 2022

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10.1002/zamm.202000275

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abstract = "In this paper, the longtime behavior of a coupled multidimensional elastic–viscoelastic waves system is considered. This model consists of an elastic wave domain and an viscoelastic wave domain, connecting by a common interface. The dissipative damping is produced in the viscoelastic wave via the boundary connection. By the resolvent estimate together with microlocal analysis argument, we show that the corresponding semigroup is polynomially stable with decay rate (Formula presented.) under certain conditions.",

author = "Han, {Zhong Jie} and Kai Yu and Qiong Zhang",

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N2 - In this paper, the longtime behavior of a coupled multidimensional elastic–viscoelastic waves system is considered. This model consists of an elastic wave domain and an viscoelastic wave domain, connecting by a common interface. The dissipative damping is produced in the viscoelastic wave via the boundary connection. By the resolvent estimate together with microlocal analysis argument, we show that the corresponding semigroup is polynomially stable with decay rate (Formula presented.) under certain conditions.

AB - In this paper, the longtime behavior of a coupled multidimensional elastic–viscoelastic waves system is considered. This model consists of an elastic wave domain and an viscoelastic wave domain, connecting by a common interface. The dissipative damping is produced in the viscoelastic wave via the boundary connection. By the resolvent estimate together with microlocal analysis argument, we show that the corresponding semigroup is polynomially stable with decay rate (Formula presented.) under certain conditions.

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Longtime behavior of multidimensional wave equation with local Kelvin–Voigt damping

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