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Evolution Equations And Approximations

Name: Evolution Equations And Approximations
Brand: World Scientific Publishing Co Pte Ltd
SKU: 05067220
Price: 201.7 EUR
Availability: InStock
Author: Kazufumi Ito
ISBN: 9789812380265

Kazufumi Ito

Franz Kappel

Language

English

Book Hardback

Libristo code: 05067220

Publishers World Scientific Publishing Co Pte Ltd, May 2002

This text presents an approximation theory for a general class of nonlinear evolution equations in B... Full description

Libristo code: 05067220

488 b

201.70 €

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This text 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 work 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 non-homogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.