Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping
We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation. © 2006 Elsevier Inc. All rights reserved.
Journal of Differential Equations
Chueshov, I., & Lasiecka, I. (2007). Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping. Journal of Differential Equations, 233 (1), 42-86. https://doi.org/10.1016/j.jde.2006.09.019