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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Bociu, Lorena²  Toundykov, Daniel¹ 

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

关键词: Plate;    Von Karman;    Irrotational;    Airy stress;    Free boundary conditions;    Boundary damping;    Non-dissipative;    Non-gradient;    Attractor;    Asymptotic smoothness;   

DOI  :  10.1016/j.jde.2012.08.004

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free