恢复三阶非线性声学方程中出现的随时间变化的非线性的逆问题 *

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-05-23 DOI:10.1088/1361-6420/ad49cd

Song-Ren Fu, Peng-Fei Yao and Yongyi Yu

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引用次数: 0

摘要

本文主要研究乔丹-摩尔-吉布森-汤普森方程（Jordan-Moore-Gibson-Thompson equation）的非线性恢复问题，这是一个三阶非线性声学方程。例如，该方程产生于波在粘性热松弛流体中的传播。利用较小的初始数据和边界数据，可以获得非线性方程的良好拟合。通过对非线性方程进行二阶线性化，并构建线性化方程的复杂几何光学解，得出了恢复非线性的唯一性。

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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Inverse problem of recovering a time-dependent nonlinearity appearing in third-order nonlinear acoustic equations *

This paper is devoted to some inverse problems of recovering the nonlinearity for the Jordan–Moore–Gibson–Thompson equation, which is a third order nonlinear acoustic equation. This equation arises, for example, from the wave propagation in viscous thermally relaxing fluids. The well-posedness of the nonlinear equation is obtained with the small initial and boundary data. By the second order linearization to the nonlinear equation, and construction of complex geometric optics solutions for the linearized equation, the uniqueness of recovering the nonlinearity is derived.

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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.