Determination of source or initial values for acoustic equations with a time-fractional attenuation

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-11-09 DOI:10.1142/s0219530523500100

Xinchi Huang, Yavar Kian, É. Soccorsi, Masahiro Yamamoto

引用次数: 0

Abstract

We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or photoacoustic tomography. We prove a stability estimate for each of these two problems, with the aid of a Carleman estimate specifically designed for the governing equation.

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具有时间分数衰减的声学方程的源或初始值的确定

研究了由非局部时间分数阶导数阻尼的双曲型方程初始状态或源项的反演问题。该框架与医学成像相关，如热声或光声断层扫描。我们利用专门为控制方程设计的Carleman估计，证明了这两个问题的稳定性估计。

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

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.