Boundary stabilization of thin plates

TLDR: In this article, the authors considered the boundary feedback stabilization of Kirchhoff plates subject to weak viscoelastic damping, and the asymptotic stability of the limit systems.

Abstract: 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 KE 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.