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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-03-20 DOI:10.1088/1361-6420/ad35e2

Alberto Mercado

引用次数: 0

Abstract

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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在ℝn中具有飞行界面的透射波方程的逆问题

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。

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

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.