Uniqueness and numerical reconstruction for inverse problems dealing with interval size search

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-09-07 DOI:10.3934/ipi.2021062

J. Apraiz, J. Cheng, A. Doubova, E. Fern'andez-Cara, M. Yamamoto

引用次数: 2

Abstract

We consider a heat equation and a wave equation in one spatial dimension. This article deals with the inverse problem of determining the size of the spatial interval from some extra boundary information on the solution. Under several different circumstances, we prove uniqueness, non-uniqueness and some size estimates. Moreover, we numerically solve the inverse problems and compute accurate approximations of the size. This is illustrated with several satisfactory numerical experiments.

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区间大小搜索逆问题的唯一性与数值重构

我们考虑一维空间中的一个热方程和一个波动方程。本文研究了利用解上的一些附加边界信息来确定空间区间大小的反问题。在几种不同的情况下，我们证明了唯一性、非唯一性和一些大小估计。此外，我们在数值上解决了反问题，并计算了尺寸的精确近似值。用几个令人满意的数值实验说明了这一点。

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 and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.