On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-08-09 DOI:10.3934/ipi.2023008

Li Li

引用次数: 4

Abstract

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the Dirichlet-to-Neumann map. We exploit the integration by parts formula for Riemann-Liouville and Caputo derivatives to derive the Runge approximation property for our space-time fractional operator based on the unique continuation property of the fractional Laplacian. This enables us to extend early unique determination results for space-fractional but time-local operators to the space-time fractional case.

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含时相关系数的非耦合时空分数算子的反问题

研究了含时相关系数的非耦合时空分数算子，并给出了相应的反问题。我们的目标是从Dirichlet-to-Neumann图的外部部分测量中确定可变系数。我们利用Riemann-Liouville导数和Caputo导数的分部积分公式，基于分数阶拉普拉斯算子的唯一延拓性质，导出了时空分数阶算子的Runge近似性质。这使我们能够将空间分数但时间局部算子的早期唯一确定结果扩展到时空分数情况。

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.