Evolution equations and approximations
著者
書誌事項
Evolution equations and approximations
（Series on advances in mathematics for applied sciences, v. 61）
World Scientific, c2002
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注記
Includes bibliographical reference(p.489-494) and index
内容説明・目次
内容説明
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.
目次
- Dissipative and maximal monotone operators
- linear semigroups
- analytic semigroups
- approximation of C-0 semigroups
- nonlinear semigroups of contractions
- locally quasi-dissipative evolution equations
- the Crandall-Pazy class
- variational formulations and Gelfand triples
- applications to concrete systems
- approximation of solutions for evolution equations
- semilinear evolution equations. Appendices: some inequalities
- convergence of Steklov means
- some technical results needed in Section 9.2.
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