从阻尼波方程无限时间圆柱体上的解的轨迹重构初始数据

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-04-24 DOI:10.1088/1361-6420/ad42cd

Seongyeon Kim, Sunghwan Moon, Ihyeok Seo

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引用次数: 0

摘要

本文考虑了两类阻尼波方程：弱阻尼方程和强阻尼方程。我们通过时空圆柱体上的解的轨迹来恢复初始速度。这个逆问题与混合医学成像技术光声断层扫描（PAT）有关。光声断层扫描是基于在感兴趣的物体内部产生声波，而光声断层扫描的数学问题之一就是从物体外部测量到的波方程的解中重建初始速度。利用球面谐波和频谱定理，我们展示了一种恢复初始速度的方法。

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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Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations

In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is based on generating acoustic waves inside of an object of interest and one of the mathematical problem in PAT is reconstructing the initial velocity from the solution of the wave equation measured on the outside of object. Using the spherical harmonics and spectral theorem, we demonstrate a way to recover the initial velocity.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.