Boundary Stabilization of Thin Plates

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.