分数阶扩散方程变阶检测的封闭方法

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-02-06 DOI:10.3934/ipi.2022036

Masaru Ikehata, Yavar Kian

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引用次数: 1

摘要

在有界区域上，研究一类由变阶时间分数扩散方程控制的逆障碍问题。未知障碍是控制方程的分数阶时间导数的空间相关变阶偏离已知齐次背景的区域。观测数据由特殊设计的狄利克雷数据的控制方程解的诺伊曼数据给出。在适当的偏差跳跃条件下，最新版本的时域封闭方法可以从观测数据中提取有关障碍物几何形状和跳跃定性性质的信息。

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The enclosure method for the detection of variable order in fractional diffusion equations

This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional time derivative of the governing equation deviates from a known homogeneous background one. The observation data is given by the Neumann data of the solution of the governing equation for a specially designed Dirichlet data. Under a suitable jump condition on the deviation, it is shown that the most recent version of the time domain enclosure method enables one to extract information about the geometry of the obstacle and a qualitative nature of the jump, from the observation data.

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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.