Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED Inverse Problems and Imaging Pub Date : 2021-12-02 DOI:10.3934/ipi.2022027

Zhi-yuan Li, Yikan Liu, Masahiro Yamamoto

引用次数: 4

Abstract

In this paper, we obtain the sharp uniqueness for an inverse \begin{document}$ x $\end{document}-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique continuation which holds for weak solutions.

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一维时间分数扩散方程的逆源问题及弱解的唯一延拓

在本文中，我们得到了逆\ begin｛document｝$x$\ end的尖锐唯一性{document}-source用最小可能的横向Cauchy数据求解具有零阶项的一维时间分数阶扩散方程的问题。关键因素是针对弱解决方案的独特延续性。

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.