ABSTRACT
Introduction In the past decade, numerous results have demonstrated that uniform decay of the energy can be obtained for elastic systems through the use of boundary dissipation. Early results focused on the case of a homogeneous, isotropic elastic body, beginning with the work of Lagnese [8-9]. In the latter, nonlinear boundary feedback, dependent on both the velocity and the tangential component of the position, was shown to uniformly stabilize the system under the assumption that the domain
was star-shaped. Extending this result to more general domains, Horn used only velocity feedback acting as a traction force along the boundary, thus eliminating the additional feedback involving the tangential derivative [5]. Initial results on anisotropic elasticity were achieved by Alabau and Komornik with the underlying assumption that the domain was spherical, thus imposing strict geometric conditions even if control was assumed to be active on the entire boundary [2].
