UNIFORM STABILIZABILITY OF A FULL VON KARMAN SYSTEM WITH NONLINEAR BOUNDARY FEEDBACK

Full von Karman system accounting for in-plane accelerations and descr ibing the transient deformations of a thin, elastic plate subject to e dge loading is considered. The energy dissipation is introduced via th e nonlinear velocity feedback acting on a part of the edge of the plat e. It is known [J. Puel and M. Tucsnak, SIAM J. Control Optim., 33 (19 95), pp. 255-273] that in the case of linear dissipation and ''star-sh aped'' domains, boundary velocity feedback with the tangential derivat ives of horizontal displacements leads to the exponential decay rates for the energy of the resulting closed loop system. The main goal of t he paper is to derive the uniform energy decay rates valid for the mod el without the above-mentioned restrictions. In particular, it is show n that simple, monotone nonlinear feedback (without the tangential der ivatives of the horizontal displacements) provides the uniform decay r ates for the energy in the absence of geometric hypotheses imposed on the controlled part of the boundary. This is accomplished by establish ing, among other things, ''sharp'' regularity results valid for the bo undary traces of solutions corresponding to this nonlinear model and b y employing a Holmgren-type uniqueness result proved recently in [V. I sakov, J. Differential Equations, 97 (1997), pp. 134-147] for the dyna mical systems of elasticity which are overdetermined on the boundary.