ABSTRACT

In this paper, we investigate the convergence rates of the inverse heat transfer problem of simultaneously determining the space-dependent reaction coefficient and the initial temperature from some additional temperature observations. The strategy is to decouple the original problem into two inverse problems: (i) recover the reaction coefficient; (ii) determine the initial temperature with the estimated reaction coefficient in the previous stage. The Tikhonov regularization method is used to reconstruct the reaction coefficient, and a new source condition is used to derive the convergence rates to the reaction coefficient. Based on the approximated reaction coefficient, the initial temperature as well as its convergence rates can be obtained by using the quasi-reversibility method.

摘要

在本文中，我们研究了通过一些额外的温度观测同时确定空间相关反应系数和初始温度的逆传热问题的收敛速度。该策略是将原问题解耦为两个逆问题：（i）恢复反应系数；(ii) 用前一阶段估计的反应系数确定初始温度。采用Tikhonov正则化方法重构反应系数，并采用新的源条件推导反应系数的收敛速度。基于近似的反应系数，可以使用准可逆方法获得初始温度及其收敛速度。