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.
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.