Nonlinear boundary stabilization of a system of anisotropic elasticity with light internal damping (Q2708679)

The purpose of this very important paper is to study a question concerning the stabilization of an anisotropic system of elasticity on a general domain containing light internal damping which is physically motivated. To uniformly stabilize the system, nonlinear boundary damping is introduced, for acting via traction forces. The nonlinear feedback control defined in terms of the velocity is applied along a portion of the boundary of the domain. Techniques used to prove the required estimates include multiplier, sharp trace regularity results and a uniqueness argument relying on Korn's inequality for the system.NEWLINENEWLINENEWLINEMain result: The author proposes the precise proofs of stability estimates (the techniques of Lasiecka and Tataru for nonlinear control are used). Due to the additional damping, exponential decay of the energy with respect to time is established.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00042].