在ℝn中具有飞行界面的透射波方程的逆问题

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-20 DOI:10.1088/1361-6420/ad35e2

Alberto Mercado

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引用次数: 0

摘要

本文研究了在任意维度的有界域内主系数不连续的波方程。通过观察相应解在部分边界上的轨迹，得到了恢复空间相关系数的逆问题的稳定性。作为速度变化和域大小的函数，我们提供了最小所需时间的精确估计。主要工具是针对传输系统的新的全局卡勒曼估计，并根据界面几何形状调整了特定的权重函数，从而获得了对最短时间的最佳估计。关键词卡勒曼不等式、布赫金-克里巴诺夫方法、传输系统。

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An inverse problem for a transmission wave equation with a ﬂat interface in ℝn

In this paper we study a wave equation with discontinuous principal coefficient within a bounded domain of arbitrary dimension. It is obtained the stability of the inverse problem of recovering a space-dependent coefficient by observing a trace of the corresponding solution on part of the boundary. We provide a precise estimate of the minimum required time, as a function of the velocity change and domain size. The main tools are new global Carleman estimates for the transmission system with a particular weight function adapted to the interface geometry, which allows to obtain an optimal estimate of the minimum time. Keywords: Carleman inequalities, Bukhgeim–Klibanov method, transmission system.

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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.