Nonlinear Functional Evolutions in Banach Spaces

Nonlinear Functional Evolutions in Banach Spaces

by Ki Sik Ha

Paperback(Softcover reprint of the original 1st ed. 2003)

$139.99
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Overview

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.

Product Details

ISBN-13: 9789048162048
Publisher: Springer Netherlands
Publication date: 12/07/2010
Edition description: Softcover reprint of the original 1st ed. 2003
Pages: 352
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Nonlinear Evolutions.- 2. Autonomous Nonlinear Functional Evolutions.- 3. Non—Autonomous Nonlinear Functional Evolutions.- 4. Quasi—Nonlinear Functional Evolutions.- References.

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