title: The concept of minimal attractor and maximal attractors of partial differential equations of the Kuramoto-Sivashinsky type.
abstract: The first part of the paper is devoted to definition of the smallest set that may be regarded as the attractor of the dissipative system. Simple properties of this set are discussed. In the second part some geometrical facts concerning attractors of the partial differential equations are revealed. They include well-known results for the two-dimensional Navier-Stokes equation and new ones for the Kuramoto-Sivashinsky and similar equations.
authors.affiliation: Department of Mathematics and Mechanics, Moscow State University, 117234 Moscow, USSR.
authors.forename: Ju. S.
authors.initials: JS
authors.lastname: Il'yashenko