کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4610959 | 1338594 | 2012 | 42 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Differential Equations - Volume 253, Issue 12, 15 December 2012, Pages 3568-3609