Electron. J. Differential Equations, Vol. 2020 (2020), No. 95, pp. 1-13.

Energy decay for variable coefficient viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary

Jianghao Hao, Mengxian Lv

Abstract:
In this article, we study a variable coefficients viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary. By constructing suitable Lyapunov functionals and using the energy compensation method, we prove that under suitable conditions on the initial data and the relaxation function, the energy of the system has an explicit and general decay rate.

Submitted December 19, 2019. Published September 17, 2020.
Math Subject Classifications: 35L70, 35B35.
Key Words: Variable coefficients; viscoelastic wave equation; acoustic boundary conditions; nonlocally reacting boundary.
DOI: 10.58997/ejde.2020.95

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Jianghao Hao
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: hjhao@sxu.edu.cn
Mengxian Lv
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: 1550432308@qq.com

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