Global attractors for von Karman evolutions with a nonlinear boundary dissipation
Dynamic von Karman equations with a nonlinear boundary dissipation are considered. Questions related to long time behaviour, existence and structure of global attractors are studied. It is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global (compact) attractor for all weak (finite energy) solutions. This result has been known in the case of full interior dissipation, but it is new in the case when the boundary damping is the main dissipative mechanism in the system. In addition, we prove that fractal dimension of the attractor is finite. The proofs depend critically on the infinite speed of propagation associated with the von Karman model considered. © 2003 Elsevier Inc. All rights reserved.
Journal of Differential Equations
Chueshov, I., & Lasiecka, I. (2004). Global attractors for von Karman evolutions with a nonlinear boundary dissipation. Journal of Differential Equations, 198 (1), 196-231. https://doi.org/10.1016/j.jde.2003.08.008