Boundary Stabilization of Thin Plates

Table of Contents

Preface
1. Introduction: orientation
Background
Connection with exact controllability
2. Thin plate models: Kirchhoff model
Mindlin-Timoshenko model
von Karman model
A viscoelastic plate model
A linear termoelastic plate model
3. Boundary feedback stabilization of Mindlin-Timoshenko plates: Orientation: existence, uniqueness, and properties of solutions
Uniform asymptotic stability of solutions
4. Limits of the Mindlin-Timoshenko system and asymptotic stability of the limit systems: Orientation
The limit of the M-T system as KÊ 0+
The limit of the M-T system as K
Study of the Kirchhoff system
Uniform asymptotic stability of solutions
Limit of the Kirchhoff system as 0+
5. Uniform stabilization in some nonlinear plate problems: Uniform stabilization of the Kirchhoff system by nonlinear feedback
Uniform asymptotic energy estimates for a von Karman plate
6. Boundary feedback stabilization of Kirchhoff plates subject to weak viscoelastic Damping: formulation of the boundary value problem
Existence, uniqueness, and properties of solutions
Asymptotic energy estimates
7. Uniform asymptotic energy estimates for thermoelastic plates: Orientation
Existence, uniqueness, regularity, and strong stability
Uniform asymptotic energy estimates
Bibliography
Index.