一类反Stefan问题中自由边界的实时跟踪

对处于融化过程中的固体，可以利用在固定边界上得到的温度和热流测量数据，实时估计固体与液体之间的动态边界。由于在实际过程中无法在液体边测量其温度和热流，因此，该类问题无法通过直接Ｓｔｅｆａｎ问题求解来得到动态边界的实时估计。将该类问题的求解归结为一类病态反Ｓｔｅｆａｎ问题的求解，给出了一种基于Ｔｈｉｋｎｏｖ调节理论的滑动区间估计算法。

Tracking of a Moving Boundary for a Type of Inverse Stefan Problems

The moving boundary of a melting solid is estimated from temperature and flux measurements performed on the cold side of the solid only. The lack of measurement in the liquid phase prevents the moving boundary to be recovered by straightforward use of the direct Stefan solution. The estimation of this moving boundary is an inverse problem that requires particular solving methods. An algorithm is used, based on a regularized least square approach, that is extended to this nonlinear case by a predictive sliding horizon technique.