论文标题
$ \ exp（a^{ - 1} t）a^{ - 1} $的衰减率在希尔伯特空间和曲柄 - 尼科尔森方案上具有光滑的初始数据
Decay Rate of $\exp(A^{-1}t)A^{-1}$ on a Hilbert Space and the Crank-Nicolson Scheme with Smooth Initial Data
论文作者
论文摘要
本文涉及$ e^{a^{ - 1} t} a^{ - 1} $的衰减速率，用于发电机$ a $ a $ a $稳定的稳定$ C_0 $ -Semigroup在Hilbert Space上。为了估计$ e^{a^{ - 1} t} a^{ - 1} $的衰减率，我们应用了一个有界的功能计算。使用此估计值和Lyapunov方程，我们还使用平滑的初始数据研究了曲柄 - 尼科森方案的量化行为。类似的参数也适用于多项式稳定的$ C_0 $ -Semigroup，其发电机是正常的。
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.
