论文标题
在一阶段Stefan问题中识别边界涌入条件
Identification of a boundary influx condition in a one-phase Stefan problem
论文作者
论文摘要
我们考虑了热方程式的一维单相逆Stefan问题。它包括从移动前部和初始状态的位置的知识中恢复边界流行条件。我们得出了一个对数稳定性估计，该估计表明反转是不稳定的。该证明基于整体方程和全体形态函数的唯一延续。我们还提出了具有正则化项的直接算法来解决非线性反问题。使用嘈杂数据的几个数值测试进行了相对误差分析。
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a logarithmic stability estimate that shows that the inversion is ill-posed. The proof is based on integral equations and unique continuation for holomorphic functions. We also proposed a direct algorithm with a regularization term to solve the nonlinear inverse problem. Several numerical tests using noisy data are provided with relative errors analysis.
