Uniform boundary stabilization of nonlinear spherical shells by using two controls only: analysis and numerical computations

The model for an elastic, dynamic, thin shallow spherical shell will be considered. The model, consisting of a nonlinear coupled system of partial differential equations (PDEs), assumes that rotational forces are negligible. One of the primary novelties of the paper is the use of semidiscrete finite element (FEM) approximations of the eigenvalues associated with the corresponding linear system of PDEs. The numerical computations are used to gain insight regarding the number of boundary controls required to uniformly stabilize the nonlinear system and provide confirmation of the theoretical results. In particular, it will be shown that the nonlinear model is uniformly stabilized with only two controls acting on the boundary instead of the usual three.