Lagnese J.E. Boundary Stabilization of Thin Plates

Society for Industrial and Applied Mathematics, Philadelphia, 1989. -185 pp. – (Studies in Applied Mathematics; 10), OCR.
The contents of this book will now be briefly described. Some background material is presented in Chapter
1. Chapter 2 is devoted to heuristic derivations of the various plate models which are studied in subsequent chapters. Asymptotic stability of solutions of the Mindlin-Timoshenko plate model under appropriate velocity feedback at the boundary is considered in Chapter
3. This model is a hyperbolic system of three equations which are coupled through a positive parameter called the shear modulus. Chapter 4 is concerned with the limits of the Mindlin-Timoshenko system as the shear modulus approaches either zero or infinity. The former limit leads to the system of linear plane elasticity, the latter to the Kirchhoft plate model, each with certain dissipative boundary conditions. Uniform asymptotic energy estimates for each system are obtained also in Chapter
4. Uniform stabilization in nonlinear plate problems is the subject of Chapter
5. Two situations are considered: that of a nonlinear feedback law coupled to linear dynamics; and a linear feedback law coupled to the von Karmen model. Of course, the two types of nonlinearities may be coupled, but at the expense of additional technical complications. The final two chapters are devoted to obtaining asymptotic energy estimates for viscoelastic plates with long-range memory and thermoelastic plates, respectively