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 (Author)
Format:	Electronic eBook
Language:	English
Published:	Singapore World Scientific Pub. Co. c2002
Series:	Series on advances in mathematics for applied sciences v. 61
Subjects:	Evolution equations / Numerical solutions Approximation theory Evolutionsgleichung Approximationstheorie
Online Access:	FHN01 Volltext
Summary:	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
Physical Description:	xiii, 498 p. ill
ISBN:	9789812777294