Compactness Methods for Nonlinear Evolutions: 2nd Edition (Hardback) book cover

Compactness Methods for Nonlinear Evolutions

2nd Edition

By Ioan I Vrabie

Chapman and Hall/CRC

264 pages

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Hardback: 9780582248724
pub: 1995-07-24
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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



About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations