Attractors for Nonlinear Autonomous Dynamical Systems.

Intro -- Attractors for Nonlinear Autonomous Dynamical Systems -- Contents -- Preface -- Preliminary -- Some Useful Inequalities -- Basic Theory of Infinite-Dimensional Dynamical Systems for Autonomous Nonlinear Evolutionary Equations -- Uniformly Compact Semigroups -- Weakly Compact Semigroups -- Ω-Limit Compact Semigroups -- Asymptotically Compact Semigroups -- Asymptotically Smooth Semigroups -- Norm-to-Weak Continuous Semigroups -- Closed Operator Semigroups -- Basic Theory of Finite-Dimensional Attractors -- The Fractal Dimension of Global Attractors -- The Estimate on Fractal Dimension of Global Attractors -- Global Attractors for the Navier-Stokes-Voight Equations with Delay -- Global Wellposedness of Solutions -- Existence of Global Attractors -- Dissipation: Existence of Absorbing Sets -- Asymptotical Compactness and Existence of Attractor -- Bibliographic Comments -- Global Attractor and Its Upper Estimate on Fractal Dimension for the 2D Navier-Stokes-Voight Equations -- Global Existence of Solutions -- Existence of Global Attractors -- Existence of Absorbing Sets -- Some Compactness and the Existence of Global Attractors -- Upper Estimate on the Fractal Dimension of Global Attractors -- Bibliographic Comments -- Maximal Attractor for the Equations of One-Dimensional Compressible Polytropic Viscous Ideal Gas -- Our Problem -- Nonlinear Semigroup on H(2) -- Existence of an Absorbing Set in H(1) β -- Existence of an Absorbing Set in H(2) β -- Proof of Theorem 4.2.1 -- Bibliographic Comments -- Universal Attractors for a Nonlinear System of Compressible One-Dimensional Heat-Conducting Viscous Real Gas -- Main Results -- Nonlinear C 0 -Semigroup on H + i (i = 1,2) -- Existence of an Absorbing Set in H1 δ -- Existence of an Absorbing Set in H 2 δ -- Proof of Theorem 5.1.1 -- Bibliographic Comments.

Global Attractors for the Compressible Navier-Stokes Equations in Bounded Annular Domains -- Main Result -- Nonlinear Semigroup on H (2) -- Existence of an Absorbing Set in H(1) δ -- Existence of an Absorbing Set in H(2) δ -- Existence of an Absorbing Set in H(4) δ -- Bibliographic Comments -- Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys -- Main Result -- An Absorbing Set Bδ in Hδ -- Compactness of the Orbit in Hδ -- Bibliographic Comments -- Global Attractors for Nonlinear Reaction-Diffusion Equations and the 2D Navier-Stokes Equations -- Global Attractor for Strong Solutions of Reaction-Diffusion Equations -- Existence of Solutions and Uniqueness -- Global Attractor for the Semigroup in Lp(Ω) -- Global Attractor of System in Lp(Ω) and H10(Ω) -- Global Attractors for the 2D Navier-Stokes Equations in H10(Ω) -- Global Attractors for an Incompressible Fluid Equation and a Wave Equation -- An Incompressible Fluid Equation -- A Wave Equation with Nonlinear Damping -- Wellposedness of Solutions -- Dissipativity -- Asymptotic Compactness and Existence of Global Attractor -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.