Stabilization of the Viscoelastic Wave Equation with Variable Coefficients and a Delay Term in Nonlocal Boundary Feedback.
- Resource Type
- Article
- Authors
- Li, Sheng-Jie; Chai, Shugen
- Source
- Journal of Dynamical & Control Systems. Mar2024, Vol. 30 Issue 1, p1-24. 24p.
- Subject
- *WAVE equation
*RIEMANNIAN geometry
*KERNEL functions
*ENERGY consumption
- Language
- ISSN
- 1079-2724
In this paper, we investigate the viscoelastic wave equation with variable coefficients and a delay, which is subject to nonlinear and nonlocal boundary dissipation. The existence of strong and weak solutions is obtained by means of Faedo-Galerkin approximation and denseness argument. By introducing an equivalent energy functional and using the Riemannian geometry method, we show the general decay rate of energy when kernel function satisfies some sufficient small conditions that we provide the range accurately. [ABSTRACT FROM AUTHOR]