Inverse problems for a half-order time-fractional diffusion equation in arbitrary dimension by Carleman estimates

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-10-20 DOI:10.3934/IPI.2021040

Xinchi Huang, A. Kawamoto

引用次数: 4

Abstract

We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish the stability estimate of Lipschitz type in the inverse problems and the proofs are based on the Bukhgeim-Klibanov method by using Carleman estimates.

查看原文本刊更多论文

用Carleman估计求解任意维半阶时间分数扩散方程的反问题

考虑任意维的半阶时间-分数扩散方程，在一些附加假设下，研究了在任意固定时间从空间数据确定源项或扩散系数的反问题。本文建立了逆问题的Lipschitz型稳定性估计，并利用Carleman估计在Bukhgeim-Klibanov方法上进行了证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.