
Compactness Methods for Nonlinear Evolutions
Ioan I. Vrabie(Author)
CRC Press
2nd Edition
Published on 24. July 1995
Book
Hardback
264 pages
978-0-582-24872-4 (ISBN)
Description
This monograph provides a self-contained and comprehensive account of the most significant existence results obtained over the
past two decades referring to some remarkable classes of ill-posed problems governed by non-accretive operators. All the results are derived from several compactness arguments, due mainly to the author, and are suitably illustrated by examples arising from various concrete problems - for example, nonlinear diffusion, heat conduction in materials with memory, fluid dynamics, and vibrations of a string with memory. Reference is made to optimal control theory in order to emphasize the degree of applicability of abstract compactness methods. Special attention is paid to multivalued perturbations of m-accretive operators; this case is analyzed under appropriate assumptions in order to allow the use of the general results in the study of some specific problems of great practical interest: reaction-diffusion and closed loop systems. Some biographical comments and open problems are also included. This new edition contains a number of improvements, corrections and insertions which both simplify and update the material. The book will be of interest to graduate students and specialists working in abstract evolution equations, partial differential equations, reaction-diffusion systems and ill-posed problems. A knowledge of topology, functional analysis and ordinary differential equations to undergraduate level is assumed.
past two decades referring to some remarkable classes of ill-posed problems governed by non-accretive operators. All the results are derived from several compactness arguments, due mainly to the author, and are suitably illustrated by examples arising from various concrete problems - for example, nonlinear diffusion, heat conduction in materials with memory, fluid dynamics, and vibrations of a string with memory. Reference is made to optimal control theory in order to emphasize the degree of applicability of abstract compactness methods. Special attention is paid to multivalued perturbations of m-accretive operators; this case is analyzed under appropriate assumptions in order to allow the use of the general results in the study of some specific problems of great practical interest: reaction-diffusion and closed loop systems. Some biographical comments and open problems are also included. This new edition contains a number of improvements, corrections and insertions which both simplify and update the material. The book will be of interest to graduate students and specialists working in abstract evolution equations, partial differential equations, reaction-diffusion systems and ill-posed problems. A knowledge of topology, functional analysis and ordinary differential equations to undergraduate level is assumed.
More details
Series
Edition
2nd New edition
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Edition type
New edition
Dimensions
Height: 280 mm
Width: 210 mm
Weight
522 gr
ISBN-13
978-0-582-24872-4 (9780582248724)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Vrabie\, Ioan I
Content
Foreword
Preface
Preface to the Second Edition
Notation and Conventions
Elements of Nonlinear Functional Analysis
Fundamental Compactness Results
Nonlinear Perturbations of Accretive Operators
Demiclosed Perturbations of Subdifferentials
Functional and Integrodifferential Equations
Bibliographical Notes, Comments and Open Problems
References
Index
Preface
Preface to the Second Edition
Notation and Conventions
Elements of Nonlinear Functional Analysis
Fundamental Compactness Results
Nonlinear Perturbations of Accretive Operators
Demiclosed Perturbations of Subdifferentials
Functional and Integrodifferential Equations
Bibliographical Notes, Comments and Open Problems
References
Index