Evolution equations and approximations

Author(s)

• Ito, Kazufumi
• Kappel, Franz

Bibliographic Information

Evolution equations and approximations

Kazufumi Ito, Franz Kappel

（Series on advances in mathematics for applied sciences, v. 61）

World Scientific, c2002

Note

Includes bibliographical reference(p.489-494) and index

Description and Table of Contents

Description

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 the Lie-Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory.In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.

Table of Contents

• Dissipative and maximal monotone operators
• linear semigroups
• analytic semigroups
• approximation of C-0 semigroups
• nonlinear semigroups of contractions
• locally quasi-dissipative evolution equations
• the Crandall-Pazy class
• variational formulations and Gelfand triples
• applications to concrete systems
• approximation of solutions for evolution equations
• semilinear evolution equations. Appendices: some inequalities
• convergence of Steklov means
• some technical results needed in Section 9.2.

by "Nielsen BookData"

Details

• NCID: BA57694297
• ISBN:
  • 9812380264
• Country Code: si
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Singapore
• Pages/Volumes: xiii, 498 p.
• Size: 23 cm
• Parent Bibliography ID:
  • BA11334635