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Global attractors and inertial manifolds for some nonlinear partial differential equations.

by Huang Yu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 145-150). / Introduction --- p.1 / Chapter 1 --- Global Attractors of Semigroups --- p.9 / Introduction --- p.9 / Chapter 1.1 --- Basic Notions --- p.9 / Chapter 1.2 --- Semigroup of Class K --- p.11 / Chapter 1.3 --- Semigroup of Class AK --- p.15 / Chapter 1.4 --- Hausdorff and Fractal Dimensions of Attractors --- p.19 / Chapter 1.4.1 --- Hausdorff and Fractal dimensions --- p.20 / Chapter 1.4.2 --- The Dimensions of Invariant Sets --- p.22 / Chapter 1.4.3 --- An Application to Evolution Equations --- p.35 / Notes --- p.39 / Chapter 2 --- Invariant Manifolds and Inertial Manifolds --- p.40 / Introduction --- p.40 / Chapter 2.1 --- Preliminary --- p.41 / Chapter 2.1.1 --- Notions --- p.41 / Chapter 2.1.2 --- Nemytskii Operator --- p.43 / Chapter 2.1.3 --- Contractions on Embedded Banach Spaces --- p.47 / Chapter 2.2 --- Linear and Nonlinear Integral Equations --- p.49 / Chapter 2.3 --- Invariant Manifolds --- p.55 / Chapter 2.4 --- Inertial Manifolds --- p.59 / Notes --- p.63 / Chapter 3 --- Semilinear Parabolic Variational Inequalities --- p.64 / Introduction --- p.64 / Chapter 3.1 --- Existence Results --- p.66 / Chapter 3.2 --- The Existence of Global Attractors --- p.69 / Chapter 3.3 --- The Weakly Approximating Inertial Manifolds --- p.76 / Chapter 3.4 --- An Application: The Obstacle Problem --- p.87 / Chapter 4 --- Semilinear Wave Equations with Damping and Critical Expo- nent --- p.91 / Introduction --- p.91 / Chapter 4.1 --- Existence Results --- p.93 / Chapter 4.2 --- The Global Attractor for the Problem --- p.96 / Chapter 4.2.1 --- A Proposition on Uniform Decay --- p.98 / Chapter 4.2.2 --- Compactness of the Trajectories of (4.2.7) --- p.102 / Chapter 4.3 --- A Particular Case-Linear Damping --- p.105 / Chapter 4.4 --- Estimate of the Dimensions of the Global Attractor --- p.111 / Chapter 4.4.1 --- The Linearized Equation --- p.114 / Chapter 4.4.2 --- The Hausdorff and Fractal Dimensions of the Attractor --- p.117 / Chapter 5 --- Partially Dissipative Evolution Equations --- p.123 / Introduction --- p.123 / Chapter 5.1 --- Basic Notions --- p.124 / Chapter 5.2 --- Semilinear Parabolic Equations and Systems --- p.128 / Chapter 5.3 --- Semilinera Hyperbolic Equation with Damping --- p.136 / Reference --- p.145

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318336
Date January 1995
ContributorsHuang, Yu, Chinese University of Hong Kong Graduate School. Division of Mathematics.
PublisherChinese University of Hong Kong
Source SetsThe Chinese University of Hong Kong
LanguageEnglish
Detected LanguageEnglish
TypeText, bibliography
Formatprint, iv, 150 leaves ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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