GLOBAL STABILIZATION OF A DYNAMIC VON KARMAN PLATE WITH NONLINEAR BOUNDARY FEEDBACK

We consider a fully nonlinear von Karman system with, in addition to t he nonlinearity which appears in the equation, nonlinear feedback cont rols acting through the boundary as moments and torques. Under the ass umptions that the nonlinear controls are continuous, monotone, and sat isfy appropriate growth conditions (however, no growth conditions are imposed at the origin), uniform decay rates for the solution are estab lished. In this fully nonlinear case, we do not have, in general, smoo th solutions even if the initial data are assumed to be very regular. However, rigorous derivation of the estimates needed to solve the stab ilization problem requires a certain amount of regularity of the solut ions which is not guaranteed. To deal with this problem, we introduce a regularization/approximation procedure which leads to an ''approxima ting'' problem for which partial differential equation calculus can be rigorously justified. Passage to the limit on the approximation recon structs the estimates needed for the original nonlinear problem.