Reconstruction of degenerate conductivity region for parabolic equations

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-15 DOI:10.1088/1361-6420/ad308a

Piermarco Cannarsa, Anna Doubova, Masahiro Yamamoto

引用次数: 0

Abstract

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of the inverse problem to the initial data. We give sufficient conditions on the initial data for uniqueness and stability for the one-point measurement and show some examples of positive and negative results. On the other hand, we present more general uniqueness results, also for the identification of an initial data by measurements distributed over time. The proofs are based on an explicit form of the solution by means of Bessel functions of the first type. Finally, the theoretical results are supported by numerical experiments.

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抛物方程退化传导区域的重构

我们考虑了一个反问题，即通过测量域边界一侧的法导数来重建一维抛物方程中扩散系数的退化点。我们分析了逆问题对初始数据的敏感性。我们给出了单点测量在初始数据上唯一性和稳定性的充分条件，并举例说明了正反结果。另一方面，我们提出了更普遍的唯一性结果，也适用于通过随时间分布的测量来识别初始数据。这些证明基于第一类贝塞尔函数的解的明确形式。最后，这些理论结果得到了数值实验的支持。

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

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.