Decay Rate of $$\varvec{\exp (A^{-1}t)A^{-1}}$$ on a Hilbert Space and the Crank–Nicolson Scheme with Smooth Initial Data

IF 0.8 3区数学 Q2 MATHEMATICS

Integral Equations and Operator Theory Pub Date : 2023-11-12 DOI:10.1007/s00020-023-02748-1

Masashi Wakaiki

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引用次数: 0

Abstract

Abstract This paper is concerned with the decay rate of $$e^{A^{-1}t}A^{-1}$$ e A - 1 t A - 1 for the generator A of an exponentially stable $$C_0$$ C 0 -semigroup on a Hilbert space. To estimate the decay rate of $$e^{A^{-1}t}A^{-1}$$ e A - 1 t A - 1 , we apply a bounded functional calculus. Using this estimate and Lyapunov equations, we also study the quantified asymptotic behavior of the Crank-Nicolson scheme with smooth initial data. A similar argument is applied to a polynomially stable $$C_0$$ C 0 -semigroup whose generator is normal.

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Hilbert空间上$$\varvec{\exp (A^{-1}t)A^{-1}}$$的衰减率及初始数据光滑的Crank-Nicolson格式

研究Hilbert空间上指数稳定的$$C_0$$ c0 -半群的生成子A的衰减率($$e^{A^{-1}t}A^{-1}$$ e A - 1)和(A - 1)。为了估计$$e^{A^{-1}t}A^{-1}$$ e A - 1 t A - 1的衰减率，我们应用了有界泛函演算。利用这个估计和Lyapunov方程，我们还研究了具有光滑初始数据的Crank-Nicolson格式的量化渐近行为。一个类似的论证被应用于多项式稳定的$$C_0$$ C 0 -半群，它的生成器是正常的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Integral Equations and Operator Theory 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Integral Equations and Operator Theory (IEOT) is devoted to the publication of current research in integral equations, operator theory and related topics with emphasis on the linear aspects of the theory. The journal reports on the full scope of current developments from abstract theory to numerical methods and applications to analysis, physics, mechanics, engineering and others. The journal consists of two sections: a main section consisting of refereed papers and a second consisting of short announcements of important results, open problems, information, etc.