Hardcover ISBN:  9780821845653 
Product Code:  MMONO/109 
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eBook ISBN:  9781470445201 
Product Code:  MMONO/109.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845653 
eBook: ISBN:  9781470445201 
Product Code:  MMONO/109.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821845653 
Product Code:  MMONO/109 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445201 
Product Code:  MMONO/109.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845653 
eBook ISBN:  9781470445201 
Product Code:  MMONO/109.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 109; 1992; 230 ppMSC: Primary 47; Secondary 35; 81
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.
ReadershipGraduate students, researchers, and professionals in science and engineering with a background in functional analysis and real analysis.

Table of Contents

Chapters

Chapter 1. Basic results of functional analysis

Chapter 2. Dissipative operators

Chapter 3. Semigroups of nonlinear contractions

Chapter 4. Generation of semigroups of nonlinear contractions

Chapter 5. Cauchy problems for evolution equations

Chapter 6. Convergence and perturbation of nonlinear semigroups

Chapter 7. Quasilinear partial differential equations of first order


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


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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 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.
Graduate students, researchers, and professionals in science and engineering with a background in functional analysis and real analysis.

Chapters

Chapter 1. Basic results of functional analysis

Chapter 2. Dissipative operators

Chapter 3. Semigroups of nonlinear contractions

Chapter 4. Generation of semigroups of nonlinear contractions

Chapter 5. Cauchy problems for evolution equations

Chapter 6. Convergence and perturbation of nonlinear semigroups

Chapter 7. Quasilinear partial differential equations of first order

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