| Description |
1 online resource |
| Contents |
Cover; Title Page; Copyright Page; Table of Contents; Preface; PART I: PRELIMINARIES; 1: Preliminaries of Functional Analysis; 1.1 Introduction to Hilbert Spaces; 1.2 Weak Topology and Weak Convergence; 1.3 Reflexive Banach Spaces; 1.4 Distributions and Sobolev Spaces; 1.4.1 Vector-valued Functions; 1.4.2 Lp Spaces; 1.4.3 Scalar Distributions and Sobolev Spaces; 1.4.4 Vector Distributions and Sobolev Spaces; 2: Convex Analysis and Subdifferential Operators; 2.1 Introduction; 2.2 Convex Sets and Convex Functions; 2.3 Continuity of Convex Functions; 2.4 Minimization Properties |
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2.5 Fenchel Subdifferential2.6 The Fenchel Conjugate; 3: Maximal Monotone Operators; 3.1 Introduction; 3.2 Monotone Operators; 3.3 Maximal Monotonicity; 3.4 Resolvent and Yosida Approximation; 3.5 Canonical Extension; PART II: EVOLUTION EQUATIONS OF MONOTONE TYPE; 4: First Order Evolution Equations; 4.1 Introduction; 4.2 Existence and Uniqueness of Solutions; 4.3 Periodic Forcing; 4.4 Nonexpansive Semigroup Generated by a Maximal Monotone Operator; 4.5 Ergodic Theorems for Nonexpansive Sequences and Curves; 4.5.1 Almost Nonexpansive Sequences; 4.5.2 Almost Nonexpansive Curves |
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4.6 Weak Convergence of Solutions and Means4.7 Almost Orbits; 4.8 Sub-differential and Non-expansive Cases; 4.9 Strong Ergodic Convergence; 4.10 Strong Convergence of Solutions; 4.11 Quasi-convex Case; 5: Second Order Evolution Equations; 5.1 Introduction; 5.2 Existence and Uniqueness of Solutions; 5.2.1 The Strongly Monotone Case; 5.2.2 The Non Strongly Monotone Case; 5.3 Two Point Boundary Value Problems; 5.4 Existence of Solutions for the Nonhomogeneous Case; 5.5 Periodic Forcing; 5.6 Square Root of a Maximal Monotone Operator; 5.7 Asymptotic Behavior; 5.7.1 Ergodic Convergence |
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5.7.2 Weak Convergence5.7.3 Strong Convergence; 5.7.4 Subdifferential Case; 5.8 Asymptotic Behavior for Some Special Nonhomogeneous Cases; 5.8.1 Case C d"0; 5.8.2 The Case C> 0; 6: Heavy Ball with Friction Dynamical System; 6.1 Introduction; 6.2 Minimization Properties; PART III: DIFFERENCE EQUATIONS OF MONOTONE TYPE; 7: First Order Difference Equations and Proximal Point Algorithm; 7.1 Introduction; 7.2 Boundedness of Solutions; 7.3 Periodic Forcing; 7.4 Convergence of the Proximal Point Algorithm; 7.5 Convergence with Non-summable Errors; 7.6 Rate of Convergence |
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8: Second Order Difference Equations8.1 Introduction; 8.2 Existence and Uniqueness; 8.3 Periodic Forcing; 8.4 Continuous Dependence on Initial Conditions; 8.5 Asymptotic Behavior for the Homogeneous Case; 8.5.1 Weak Ergodic Convergence; 8.5.2 Strong Ergodic Convergence; 8.5.3 Weak Convergence of Solutions; 8.5.4 Strong Convergence of Solutions; 8.6 Subdifferential Case; 8.7 Asymptotic Behavior for the Non-Homogeneous Case; 8.7.1 Mean Ergodic Convergence; 8.7.2 Weak Convergence of Solutions; 8.7.3 Strong Convergence of Solutions; 8.8 Applications to Optimization |
| Summary |
This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors |
| Notes |
"A science publishers book." |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Behzad Djafari Rouhani |
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Print version record |
| Subject |
Evolution equations, Nonlinear.
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Differential equations, Nonlinear.
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Differential equations.
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Hilbert space.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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MATHEMATICS -- Functional Analysis.
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SCIENCE -- Life Sciences -- General.
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MATHEMATICS -- Differential Equations.
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Differential equations
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Differential equations, Nonlinear
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Evolution equations, Nonlinear
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Hilbert space
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| Form |
Electronic book
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| Author |
Khatibzadeh, Hadi, author
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| ISBN |
9780429156908 |
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0429156901 |
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9780429528880 |
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0429528884 |
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9781482228199 |
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148222819X |
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9780429543586 |
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0429543581 |
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