Translations of Mathematical Monographs 1992; 230 pp; hardcover Volume: 109 ISBN10: 0821845659 ISBN13: 9780821845653 List Price: US$103 Member Price: US$82.40 Order Code: MMONO/109
 This book presents a systematic exposition of the general theory of nonlinear contraction semigroups in Banach spaces and is aimed at students and researchers in science and engineering as well as in mathematics. Suitable for use as a textbook in graduate courses and seminars, this selfcontained book is accessible to those with only a basic knowledge of functional analysis. After prerequisites presented in the first chapter, Miyadera covers the basic properties of dissipative operators and nonlinear contraction semigroups in Banach spaces. The generation of nonlinear contraction semigroups, the Komura theorem, and the CrandallLiggett theorem are explored, and there is a treatment of the convergence of difference approximations of Cauchy problems for \(\omega\)dissipative operators and the Kobayashi generation theorem of nonlinear semigroups. Nonlinear Semigroups concludes with applications to nonlinear evolution equations and to firstorder quasilinear equations. Readership Graduate students, researchers, and professionals in science and engineering with a background in functional analysis and real analysis. Reviews "the author, a leading researcher in the field, presents a quite elegant and systematic treatment of the theory of nonlinear semigroups in general Banach spaces with applications to nonlinear evolution equations ... I would like to express my regret that it took so many years for the English version of this useful book to appear."  Mathematical Reviews "A good source of information for all those interested in the theory of nonlinear semigroups."  Zentralblatt MATH Table of Contents  Basic results of functional analysis
 Dissipative operators
 Semigroups of nonlinear contractions
 Generation of semigroups of nonlinear contractions
 Cauchy's problems for evolution equations
 Convergence and perturbation of nonlinear semigroups
 Quasilinear partial differential equations of first order
