CONDITIONAL STABILITY AND NUMERICAL RECONSTRUCTION OF INITIAL TEMPERATURE
CONDITIONAL STABILITY AND NUMERICAL RECONSTRUCTION OF INITIAL TEMPERATURE
复制标题
DOI：
10.3934/cpaa.2009.8.361
复制
发表时间：
2008-10
影响因子：
1
通讯作者：
Jingzhi Li;Masahiro Yamamoto;J. Zou
中科院分区：
文献类型：
--
作者：
Jingzhi Li;Masahiro Yamamoto;J. Zou
在本文中，我们解决了在有温度测量数据的情况下，导热系统初始温度的反演问题，这些温度测量数据可能是在物理域内或边界上的一个子区域，沿着一个可能开始于某个点的时间段，可能远离初始时间。首先用Carleman估计得到了这种重构的条件稳定性估计。提出了基于输出最小二乘公式和Tikhonov正则化的有限元离散化数值重建算法，并给出了有限元解的存在性和收敛性。数值实验验证了该方法的适用性和有效性。
In this paper, we address an inverse problem of reconstruction of the initial temperature in a heat conductive system when some measurement data of temperature are available, which may be observed in a subregion inside or on the boundary of the physical domain, along a time period which may start at some point, possibly far away from the initial time. A conditional stability estimate is first achieved by the Carleman estimate for such reconstruction. Numerical reconstruction algorithm is proposed based on the output least-squares formulation with the Tikhonov regularization using the finite element discretization, and the existence and convergence of the finite element solution are presented. Numerical experiments are carried out to demonstrate the applicability and effectiveness of the proposed method.