UNIFORM BOUNDARY STABILIZATION OF A NONLINEAR SHALLOW AND THIN ELASTIC SPHERICAL CAP

A coupled nonlinear system describing the vibrations of a shallow thin spherical shell is considered. It is shown that if the ''thickness'' parameter h/rho(0) is large with respect to the ''shallowness'' parame ter Q(0) = rho(0)/R, then the dissipative feedback applied at the boun dary of the shell causes the energy of the system to decay to zero at an uniform rate. The limitations on the values of these physical param eters are confirmed by the static nonlinear theory which predicts, for small values of the thickness parameter, the existence of multiple eq uilibrium states (everted stares). (C) 1996 Academic Press, Inc.