THE ENCLOSURE METHOD FOR THE DETECTION OF VARIABLE ORDER IN FRACTIONAL DIFFUSION EQUATIONS

被引：2

作者：

Ikehata, Masaru ^{[1
,2
]}

Kian, Yavar ^{[3
]}

机构：

[1] Hiroshima Univ, Lab Math, Grad Sch Adv Sci & Engn, Higashihiroshima 7398527, Japan

[2] Gunma Univ, Maebashi, Gumma 3718510, Japan

[3] Aix Marseille Univ, CNRS, CPT, Univ Toulon, Marseille, France

来源：

INVERSE PROBLEMS AND IMAGING | 2023年 / 17卷 / 01期

基金：

日本学术振兴会;

关键词：

inverse problem; time-fractional diffusion equation; space-dependent variable order; anomalous diffusion; Enclosure method; DOMAIN;

D O I：

10.3934/ipi.2022036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 variableorder 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.

引用

页码：180 / 202

页数：23

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