State observation problem for general time reversible system and applications
State observation problem for general time reversible system and applications
复制标题
DOI：
10.1016/j.amc.2010.08.020
复制
发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
Jing Li;Qi Lü
中科院分区：
文献类型：
--
作者：
Jing Li;Qi Lü
本文研究一般时间可逆系统的状态观测问题，即，从合适的观测数据中恢复给定系统的初始状态。提出了一个抽象的统一框架。利用迭代时间反演技术，我们得到了两个具有显式收敛速度的近似重建初始状态的渐近公式。一般的结果，然后应用到状态观测问题的薛定谔方程和波动方程。
This paper is concerned with a state observation problem for the general time reversible system, i.e., to recover the initial state of the given system from suitable observation data. An abstract unified framework is presented. By means of an iterative time reversal technique, we derive two asymptotic formulae of reconstructing the initial state approximately with explicit convergence rates. General results are then applied to the state observation problems for the Schrödinger equation and the wave equation.