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Nonlinear Semigroups
Isao Miyadera
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Translations of Mathematical Monographs
1992; 230 pp; hardcover
Volume: 109
ISBN-10: 0-8218-4565-9
ISBN-13: 978-0-8218-4565-3
List Price: US$98
Member Price: US$78.40
Order Code: MMONO/109
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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 self-contained 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 Crandall-Liggett 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 first-order 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
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