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arXiv · 2204.03170

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

Masashi Wakaiki
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Abstract

This paper is concerned with the decay rate of $e^{A^{-1}t}A^{-1}$ for the generator $A$ of an exponentially stable $C_0$-semigroup on a Hilbert space. To estimate the decay rate of $e^{A^{-1}t}A^{-1}$, 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 $C_0$-semigroup whose generator is normal.

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Masashi Wakaiki. 2022-04-07. Decay Rate of $\exp(A^{-1}t)A^{-1}$ on a Hilbert Space and the Crank-Nicolson Scheme with Smooth Initial Data. https://doi.org/10.1007/s00020-023-02748-1

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