Evolution Equations and Approximations 1st Edition by Kazufumi Ito (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review Ito and Kappel offer a unified presentation of the general approach for well-posedness results using abstract evolution equations. — Book News, Inc., 2002

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The given book provides a very detailed insight into the topic evolution equations. But, not only the results are very detailed, the proofs as well. It could be a basis for a student seminar. The book is beside standard results from Linear Functional- and Complex- Analysis self contained. Especially, due to its detailed view on the different existence theory of nonautonomous evolution equations it is a must for nonlinear functional analysts.

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