Finite-dimensional attractors of weak solutions to von Karman plate model
Asymptotic behavior of solutions to a von Karman dissipative system with nonlinear dissipation is considered. In the case where only boundary dissipation is present, existence of local compact attractors is established. In the case of interior dissipation, instead, it is shown that the compact attractor is also global. It is also shown that these attractors are of finite Hausdorff dimension (with explicit estimates for their dimensions). The novelty and difficulty of the problem stems from the fact that the nonlinear term in the equation is not a compact perturbation (unlike other von Karman models which account for rotational forces).
Journal of Mathematical Systems, Estimation, and Control
Lasiecka, I. (1997). Finite-dimensional attractors of weak solutions to von Karman plate model. Journal of Mathematical Systems, Estimation, and Control, 7 (3), 251-275. Retrieved from https://digitalcommons.memphis.edu/facpubs/4684