Attractors for non-dissipative irrotational von Karman plates with boundary damping

Long-time behavior of solutions to a von Karman plate equation is considered. The system has an unrestricted first-order perturbation and a nonlinear damping acting through free boundary conditions only.This model differs from those previously considered (e.g. in the extensive treatise (Chueshov and Lasiecka, 2010 11])) because the semi-flow may be of a non-gradient type: the unique continuation property is not known to hold, and there is no strict Lyapunov function on the natural finite-energy space. Consequently, global bounds on the energy, let alone the existence of an absorbing ball, cannot be a priori inferred. Moreover, the free boundary conditions are not recognized by weak solutions and some helpful estimates available for clamped, hinged or simply-supported plates cannot be invoked.It is shown that this non-monotone flow can converge to a global compact attractor with the help of viscous boundary damping and appropriately structured restoring forces acting only on the boundary or its collar.