Local and Global Compact Attractors Arising in Nonlinear Elasticity: The Case of Noncompact Nonlinearity and Nonlinear Dissipation

Asymptotic behavior of solutions to a von Kármán system with nonlinear dissipation is considered. In the case of boundary dissipation alone, existence of local compact attractors is established. Instead, in the case of interior dissipation, it is shown that the compact attractor is also global. The novelty and difficulty of the problem stems from the fact that the nonlinear and nondissipative term in the equation is not a compact perturbation (unlike other von Kármán models which account for rotational forces).