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OverviewThis book is devoted to the study of nonlinear evolution and difference equations of first and second order governed by a maximal monotone operator. This class of abstract evolution equations contains not only a class of ordinary differential equations, but also unify some important partial differential equations, such as the heat equation, wave equation, Schrodinger equation, etc. In addition to their applications in ordinary and partial differential equations, this class of evolution equations and their discrete version of difference equations have found many applications in optimization. In recent years, extensive studies have been conducted in the existence and asymptotic behaviour of solutions to this class of evolution and difference equations, including some of the authors works. This book contains a collection of such works, and its applications. Key selling features: Discusses in detail the study of non-linear evolution and difference equations governed by maximal monotone operator Information is provided in a clear and simple manner, making it accessible to graduate students and scientists with little or no background in the subject material Includes a vast collection of the authors' own work in the field and their applications, as well as research from other experts in this area of study Full Product DetailsAuthor: Behzad Djafari Rouhani , Hadi KhatibzadehPublisher: Taylor & Francis Ltd Imprint: CRC Press Weight: 0.453kg ISBN: 9780367780128ISBN 10: 0367780127 Pages: 240 Publication Date: 31 March 2021 Audience: College/higher education , General/trade , Tertiary & Higher Education , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsTable 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 EquationsReviewsAuthor InformationBIOGRAPHIES: Behzad Djafari Rouhani received his PhD degree from Yale University in 1981, under the direction of the late Professor Shizuo Kakutani. He is currently a Professor of Mathematics at the University of Texas at El Paso, USA. Hadi Khatibzadeh received his PhD degree form Tarbiat Modares University in 2007, under the direction of the first author. He is currently an Associate Professor of Mathematics at University of Zanjan, Iran. They both work in the field of Nonlinear Analysis and its Applications, and they each have over 50 refereed publications. Narcisa Apreutesei Tab Content 6Author Website:Countries AvailableAll regions |
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