Local data inverse problem for the polyharmonic operator with anisotropic perturbations

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-19 DOI:10.1088/1361-6420/ad3164

Sombuddha Bhattacharyya, Pranav Kumar

引用次数: 0

Abstract

In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input can be prescribed nor the output can be measured. We prove the unique determination of all the tensorial coefficients of the operator from the knowledge of the Dirichlet and Neumann map on the accessible part of the boundary, under suitable geometric assumptions on the domain.

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具有各向异性扰动的多谐算子的局部数据逆问题

在本文中，我们研究了一个线性多谐算子的局部数据逆问题，该算子具有多个低阶张量扰动。我们认为我们的领域有一个无法进入的边界部分，在该部分既无法规定输入，也无法测量输出。我们证明了在适当的几何假设条件下，根据对边界可进入部分的狄利克特图和诺依曼图的了解，可以唯一确定算子的所有张量系数。

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.