分数阶扩散方程变阶检测的封闭方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.