2nd Edition

Compactness Methods for Nonlinear Evolutions

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ISBN 9780582248724
Published July 24, 1995 by Chapman and Hall/CRC
264 Pages

USD $190.00

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Book 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.

Table of Contents

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

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Vrabie\, Ioan I