Nonlinear Functional Evolutions in Banach Spaces - Hardcover

Reseña del editor

There are many problems in nonlinear partial differential equations with delay which arise from, for example, physical models, biochemical models, and social models. Some of them can be formulated as nonlinear functional evolutions in infinite-dimensional abstract spaces. Since Webb (1976) considered autonomous nonlinear functional evo­ lutions in infinite-dimensional real Hilbert spaces, many nonlinear an­ alysts have studied for the last nearly three decades autonomous non­ linear functional evolutions, non-autonomous nonlinear functional evo­ lutions and quasi-nonlinear functional evolutions in infinite-dimensional real Banach spaces. The techniques developed for nonlinear evolutions in infinite-dimensional real Banach spaces are applied. This book gives a detailed account of the recent state of theory of nonlinear functional evolutions associated with accretive operators in infinite-dimensional real Banach spaces. Existence, uniqueness, and stability for 'solutions' of nonlinear func­ tional evolutions are considered. Solutions are presented by nonlinear semigroups, or evolution operators, or methods of lines, or inequalities by Benilan. This book is divided into four chapters. Chapter 1 contains some basic concepts and results in the theory of nonlinear operators and nonlinear evolutions in real Banach spaces, that play very important roles in the following three chapters. Chapter 2 deals with autonomous nonlinear functional evolutions in infinite-dimensional real Banach spaces. Chapter 3 is devoted to non-autonomous nonlinear functional evolu­ tions in infinite-dimensional real Banach spaces. Finally, in Chapter 4 quasi-nonlinear functional evolutions are con­ sidered in infinite-dimensional real Banach spaces.

Reseña del editor

There are many problems in partial differential equations with delay which arise from physical models with delay, biochemical models with delay and diffused population with delay. Some of them can be considered as nonlinear functional evolutions in appropriate infinite dimensional spaces.

While other publications in the same field have treated linear functional evolutions and nonlinear functional evolutions in finite dimensional spaces, this book is one of the first to give a detailed account of the recent state of the theory of nonlinear functional evolutions associated with multi-valued operators in infinite dimensional real Banach spaces. The techniques developed for nonlinear evolutions in real Banach spaces are applied in this book.

This book will benefit graduate students and researchers working in such diverse fields as mathematics, physics, biochemistry, and sociology who are interested in the development and application of nonlinear functional evolutions. This volume will also be useful as supplementary reading for biologists and engineers.