Determination of a Time-Dependent Free Boundary in a Two-Dimensional Parabolic Problem

被引：0

作者：

Huntul M.J. ^{[1
,2
]}

Lesnic D. ^{[1
]}

机构：

[1] Department of Applied Mathematics, University of Leeds, Leeds

[2] Department of Mathematics, College of Science, Jazan University, Jazan

来源：

International Journal of Applied and Computational Mathematics | 2019年 / 5卷 / 4期

关键词：

Free boundary; Inverse problem; Two-dimensional parabolic equation;

D O I：

10.1007/s40819-019-0700-5

中图分类号：

学科分类号：

摘要：

The retrieval of the timewise-dependent intensity of a free boundary and the temperature in a two-dimensional parabolic problem is, for the first time, numerically solved. The measurement, which is sufficient to provide a unique solution, consists of the mass/energy of the thermal system. A stability theorem is proved based on the Green function theory and Volterra’s integral equations of the second kind. The resulting nonlinear minimization is numerically solved using the lsqnonlin MATLAB optimization routine. The results illustrate the reliability, in terms of accuracy and stability, of the time-dependent free surface reconstruction. © 2019, Springer Nature India Private Limited.

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