Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 95, pp. 1-13.

Title: Energy decay for variable coefficient viscoelastic wave equation with 
       acoustic boundary conditions in domains with nonlocally reacting boundary
       
Authors: Jianghao Hao (Shanxi Univ., Taiyuan, Shanxi, China)
         Mengxian Lv  (Shanxi Univ., Taiyuan, Shanxi, China)

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.