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Nonlinear Functional Evolutions in Banach Spaces (Hardcover, 2003 ed.)
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Nonlinear Functional Evolutions in Banach Spaces (Hardcover, 2003 ed.)
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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."
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