This book is concerned with nonlinear semigroups of contractions in
Banach spaces and their application to the existence theory for
differential equa- tions associated with nonlinear dissipative
operators. The study of nonlinear semi groups resulted from the
examination of nonlinear parabolic equations and from various nonlinear
boundary value problems. The first work done by Y. Komura stimulated
much further work and interest in this subject. Thus a series of studies
was begun and then continued by T. Kato, M. G. Crandall, A. Pazy, H.
Brezis and others, who made important con- tributions to the development
of the theory. The theory as developed below is a generalisation of the
Hille-Yosida theory for one-parameter semigroups of linear operators and
is a collection of diversified results unified more or less loosely by
their methods of approach. This theory is also closely related to the
theory of nonlinear monotone operators. Of course not all aspects of
this theory could be covered in our expo- sition, and many important
contributions to the subject have been excluded for the sake of brevity.
We have attempted to present the basic results to the reader and to
orient him toward some of the applications. This book is intended to be
self-contained. The reader is assumed to have only a basic knowledge of
functional analysis, function theory and partial differential equations.
Some of the necessary prerequisites for the reading of this 'book are
summarized, with or without proof, in Chapter I.