1.

Record Nr.

UNINA9910450915003321

Autore

Ito Kazufumi

Titolo

Evolution equations and approximations [[electronic resource] /] / Kazufumi Ito, Franz Kappel

Pubbl/distr/stampa

River Edge, N.J., : World Scientific, c2002

ISBN

981-277-729-6

Descrizione fisica

1 online resource (518 p.)

Collana

Series on advances in mathematics for applied sciences ; ; v. 61

Altri autori (Persone)

KappelF

Disciplina

515/.353

Soggetti

Evolution equations - Numerical solutions

Approximation theory

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. 489-492) and index.

Nota di contenuto

Contents               ; Preface              ; Chapter 1. Dissipative and Maximal Monotone Operators                                                            ; 1.1 Duality mapping and directional derivatives of norms                                                               ; 1.2 Dissipative operators                                ; 1.3 Properties of m-dissipative operators                                                ; 1.4 Perturbation results for m-dissipative operators

1.5 Maximal monotone operators                                     1.6 Convex functionals and subdifferentials                                                  ; Chapter 2. Linear Semigroups                                   ; 2.1 Examples and basic definitions                                         ; 2.2 Cauchy problems and mild solutions                                             ; 2.3 The Hille-Yosida theorem                                   ; 2.4 The Lumer-Phillips theorem                                     ; 2.5 A second order equation

Chapter 3. Analytic Semigroups                                     3.1 Dissipative operators and sesquilinear forms                                                       ; 3.2 Analytic semigroups                              ; Chapter 4. Approximation of Co-Semigroups                                                ; 4.1 The Trotter-Kato theorem                                   ; 4.2 Approximation of nonhomogeneous problems                                                   ; 4.3 Variational formulations of the Trotter-Kato theorem

4.4 An approximation result for analytic semigroups                                                          Chapter 5. Nonlinear Semigroups of Contractions                                                      


; 5.1 Generation of nonlinear semigroups                                             ; 5.2 Cauchy problems with dissipative operators                                                     ; 5.3 The infinitesimal generator                                      ; 5.4 Nonlinear diffusion

Chapter 6. Locally Quasi-Dissipative Evolution Equations                                                               6.1 Locally quasi-dissipative operators                                              ; 6.2 Assumptions on the operators A(t)                                            ; 6.3 DS-approximations and fundamental estimates                                                      ; 6.4 Existence of DS-approximations                                         ; 6.5 Existence and uniqueness of mild solutions

6.6 Autonomous problems

Sommario/riassunto

This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.  The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and