Global attractors for von Karman evolutions with a nonlinear boundary dissipation.
The paper deals with a nonlinear system of dynamic elasticity described by the von Karman equation with a nonlinear boundary dissipation. The goal of the author is to obtain existence of a global attractor and to determine its structure. The authors prove finite dimensionality of a global attractor. Here they use a new approach to obtain finite fractal dimensionality of an attractor without using some differentiability of the corresponding semigroups. The ``infinite speed of propagation'' corresponding to the plate problems without rotational inertia play a crucial role in the authors' considerations. They conclude the paper by listing several open problems.
scientific article; zbMATH DE number 2062720
scientific article