Stabilization of the Viscoelastic Wave Equation with Variable Coefficients and a Delay Term in Nonlocal Boundary Feedback

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...

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Bibliographic Details
Published inJournal of dynamical and control systems Vol. 30; no. 1
Main Authors Li, Sheng-Jie, Chai, Shugen
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2024
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Control
Decay rate
Dynamical Systems
Dynamical Systems and Ergodic Theory
Kernel functions
Mathematics
Mathematics and Statistics
Systems Theory
Vibration
Viscoelasticity
Wave equations
Memory kernel function
35B35
93D15
Viscoelastic wave equation
Riemannian geometry method
35L05
Variable coefficient
Nonlinear and nonlocal damping
Delay
35L20
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-023-09673-x