An inverse problem of Robin coefficient identification in parabolic equations with interior degeneracy from terminal observation data

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-13 DOI:10.1016/j.apnum.2025.02.007

H. Ould Sidi , A.S. Hendy , M.M. Babatin , L. Qiao , M.A. Zaky

引用次数: 0

Abstract

In this work, we determine the unknown Robin coefficient in a degenerate parabolic equation. In inverse analysis, the problem under consideration is nonlinear with an ill-formulated operator and nonlocal. For the stable identification of the unknown Robin coefficient, the inverse problem is formulated into a regularised optimization problem. We discuss a variety of practical challenges associated with the problem. The finite element approximation is used to discretize the continuous optimization problem. The convergence and stability analyses are also discussed. Morozov's discrepancy principle is used with the conjugate gradient procedure to construct an iterative scheme. Finally, experiment results are reported to demonstrate the efficiency of the proposed schemes.

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基于终端观测资料的内简并抛物方程Robin系数辨识反问题

在这项工作中，我们确定了一个退化抛物方程的未知罗宾系数。在逆分析中，所考虑的问题是具有病态算子和非局部算子的非线性问题。对于未知Robin系数的稳定辨识，将反问题转化为正则化优化问题。我们讨论了与这个问题相关的各种实际挑战。采用有限元逼近法对连续优化问题进行离散化处理。讨论了算法的收敛性和稳定性分析。利用Morozov差异原理和共轭梯度法构造迭代格式。最后，通过实验验证了所提方案的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.