Global attractors of multivalued dynamical systems and evolution equations without uniqueness

Description

Kapustyan O.V., Mel’nik V.S, Valero J., Yasinsky V.V. - Kyiv: Naukova dumka, 2008. - 215 p.Излагается теория глобальных аттракторов бесконечномерных многозначных динамических систем. Рассматриваются приложения теории к автономным задачам математической физики. Исследованы система реакции-диффузии, система фазово-полевых уравнений, трехмерная система Навье-Стокса и эволюционное дифференциальное включение с нелипшицевой правой частью. Abstract theory of global attractors of multi-valued semiflows: Basic definitions and existence of attractors . Properties of the global attractor. Finite-dimensionality of global attractors of multi-valued semiflows. Reaction-diffusion equations: Existence and properties of solutions. Construction of the multi-valued semiflow and existence of the global attractor. System of phase-field equations: Existence and properties of solutions. Construction of the multi-valued semiflow and existence of a global attractor. 3D Navier-Stokes equations: Existence of continuous solutions: a conditional result. Existence of a strong attractor: a conditional result. Existence of a weak attractor . The Kneser property. Weak connectedness of the weak attractor. Differential inclusions: Existence and properties of solutions. Existence and properties of the global attractor. Estimate of the fractal dimension of the global attractor.