Behzad Djafari Rouhani

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 450
• Erscheinungstermin: 20. Mai 2019
• Englisch
• ISBN-13: 9780429528880
• Artikelnr.: 56139015

Autorenporträt

Behzad Djafari Rouhani

Inhaltsangabe

Table of Contents:
PART I. PRELIMINARIES
Preliminaries of Functional Analysis
Introduction to Hilbert Spaces
Weak Topology and Weak Convergence
Reexive Banach Spaces
Distributions and Sobolev Spaces
Convex Analysis and Subdifferential Operators
Introduction
Convex Sets and Convex Functions
Continuity of Convex Functions
Minimization Properties
Fenchel Subdifferential
The Fenchel Conjugate
Maximal Monotone Operators
Introduction
Monotone Operators
Maximal Monotonicity
Resolvent and Yosida Approximation
Canonical Extension
PART II - EVOLUTION EQUATIONS OF MONOTONE TYPE
First Order Evolution Equations
Introduction
Existence and Uniqueness of Solutions
Periodic Forcing
Nonexpansive Semigroup Generated by a Maximal Monotone Operator
Ergodic Theorems for Nonexpansive Sequences and Curves
Weak Convergence of Solutions and Means
Almost Orbits
Sub-differential and Non-expansive Cases
Strong Ergodic Convergence
Strong Convergence of Solutions
Quasi-convex Case
Second Order Evolution Equations
Introduction
Existence and Uniqueness of Solutions
Two Point Boundary Value Problems
Existence of Solutions for the Nonhomogeneous Case
Periodic Forcing
Square Root of a Maximal Monotone Operator
Asymptotic Behavior
Asymptotic Behavior for some Special Nonhomogeneous Cases
Heavy Ball with Friction Dynamical System
Introduction
Minimization Properties
PART III. DIFFERENCE EQUATIONS OF MONOTONE TYPE
First Order Difference Equations and Proximal Point Algorithm
Introduction
Boundedness of Solutions
Periodic Forcing
Convergence of the Proximal Point Algorithm
Convergence with Non-summable Errors
Rate of Convergence
Second Order Difference Equations
Introduction
Existence and Uniqueness
Periodic Forcing
Continuous Dependence on Initial Conditions
Asymptotic Behavior for the Homogeneous Case
Subdifferential Case
Asymptotic Behavior for the Non-Homogeneous Case
Applications to Optimization
Discrete Nonlinear Oscillator Dynamical System and the Inertial Proximal
Algorithm
Introduction
Boundedness of the Sequence and an Ergodic Theorem
Weak Convergence of the Algorithm with Errors
Subdifferential Case
Strong Convergence
PART IV. APPLICATIONS
Some Applications to Nonlinear Partial Differential Equations and
Optimization
Introduction
Applications to Convex Minimization and Monotone Operators
Application to Variational Problems
Some Applications to Partial Differential Equations