Compactness Methods for Nonlinear Evolution (Pitman Monograph & Surveys in Pure & Applied Mathematics) - Hardcover

Vrabie, I. I.

Hardcover

ISBN 10: 0582003199 ISBN 13: 9780582003194

Publisher: Longman, 1987

Synopsis

This volume provides a systematic and self-contained account of the most significant results obtained over the last ten years in an important area of nonlinear analysis: the existence theory for strongly nonlinear evolution equations governed by non-accretive perturbations of m-accretive operators. The results are derived from a small number of compactness arguments, due mainly to the author, and their use is demonstrated by examples arising from various real problems, for example, nonlinear diffusion, heat conduction in materials with memory, vibrations of a string with memory and fluid dynamics. Reference is made to optimal control theory to emphasize the applicability of abstract compactness methods. Special attention is paid to multivalued perturbations of m-accretive operators; this case is analysed under appropriate assumptions so that the abstract results can be used in some problems of great practical interest, that is, reaction-diffusion and closed loop systems. Some open problems and bibliographical comments are also included.
The book will be of interest to graduate students and those workers specializing in abstract nonlinear evolution equations with the emphasis on ill-posed problems or parabolic and hyperbolic partial differential equations, fluid dynamics, heat transfer, reaction-diffusion systems and optimal control theory.
A knowledge of topology, functional analysis and ordinary differential equations to undergraduate level is assumed.

Edition details

• Publisher: Longman
• Publication date: 1987
• Language: English
• ISBN 10: 0582003199
• ISBN 13: 9780582003194
• Binding: Hardcover
• Number of pages: 356