Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains

This paper is a study of an abstract model of a second-order non-linear elliptic boundary-value problem in a cylindrical domain by the methods of the theory of dynamical systems. It is shown that, under some natural conditions, the essential solutions of the problem in question are described by means of the global attractor of the corresponding trajectory dynamical system, and this attractor can have infinite fractal dimension and infinite topological entropy. Moreover, sharp upper and lower bounds are obtained for the Kolmogorov $\varepsilon$-entropy of these attractors.