Evolution Equations and Approximations.

Evolution Equations and Approximations.

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...

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Bibliographic Details
Main Author: Ito, Kazufumi
Other Authors: Kappel, F.
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2002.
Series:Series on advances in mathematics for applied sciences.
Subjects:
Approximation theory.
Evolution equations > Numerical solutions.
Approximation theory
Evolution equations > Numerical solutions
Online Access:Click for online access
Table of 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.

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