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Evolution Equations and Approximations by Kazufumi Ito, Franz Kappel is a nonfiction available to read on EtoBox.

What is Evolution Equations and Approximations about?

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.

Who reads Evolution Equations and Approximations?

Author

Kazufumi Ito, Franz Kappel

Publisher

World Scientific Publishing Co Pte Ltd

Published

2002

Language

EN

ISBN

9789812777294

Category

nonfiction

Subjects

Mathematics, Science, Stem