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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Evolution Equations And Approximations
• Author: Kazufumi Ito, Franz Kappel
• Language: English
• Binding: Hardback
• Number of pages: 520
• EAN: 9789812380265
• ISBN: 9812380264
• ID: 05067220
• Publisher: World Scientific Publishing Co Pte Ltd
• Weight: 871 g
• Dimensions: 229 × 157 × 32 mm
• Date of publishing: 28. May 2002

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