Nonlinear Functional Evolutions in Banach Spaces

✍ Scribed by Ki Sik Ha (auth.)

• Publisher: Springer Netherlands
• Year: 2003
• Tongue: English
• Leaves: 358
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Nonlinear Evolutions....Pages 1-30
Autonomous Nonlinear Functional Evolutions....Pages 31-126
Non—Autonomous Nonlinear Functional Evolutions....Pages 127-247
Quasi—Nonlinear Functional Evolutions....Pages 249-340
Back Matter....Pages 341-352

✦ Subjects

Difference and Functional Equations; Operator Theory; Partial Differential Equations; Ordinary Differential Equations; Integral Equations