Details

Autor(en) / Beteiligte

• Ha, Ki Sik

Titel

Nonlinear Functional Evolutions in Banach Spaces [Elektronische Ressource]

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

2003

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 evolutions in infinite-dimensional real Hilbert spaces, many nonlinear analysts have studied for the last nearly three decades autonomous nonlinear functional evolutions, non-autonomous nonlinear functional evolutions 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 functional 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 evolutions in infinite-dimensional real Banach spaces. Finally, in Chapter 4 quasi-nonlinear functional evolutions are considered in infinite-dimensional real Banach spaces