Evolution Equations And Approximations: 61 (Series on Advances in Mathematics for Applied Sciences) - Hardcover

Ito, Kazufumi; Kappel, Franz

Hardcover

ISBN 10: 9812380264 ISBN 13: 9789812380265

Publisher: World Scientific Publishing Co Pte Ltd, 2002

Synopsis

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.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 2002
• Language: English
• ISBN 10: 9812380264
• ISBN 13: 9789812380265
• Binding: Hardcover
• Number of pages: 520