一类耦合Korteweg-de Vries方程组输运系数反演问题的Lipschitz稳定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 740-761.

一类耦合Korteweg-de Vries方程组输运系数反演问题的Lipschitz稳定性

吴斌*(),陈群

^{南京信息工程大学数学与统计学院南京 210044}

收稿日期:2020-03-23 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 吴斌 E-mail:binwu@nuist.edu.cn
基金资助:
国家自然科学基金(11601240)

Lipschitz Stability for a Transport Coefficient Inverse Problem of a Linearly Coupled Korteweg-de Vries System

Bin Wu*(),Qun Chen

^{School of Mathematics and Statistics, College of Science, Nanjing University of Information Science and Technology, Nanjing 210044}

Received:2020-03-23 Online:2021-06-26 Published:2021-06-09
Contact: Bin Wu E-mail:binwu@nuist.edu.cn
Supported by:
the NSFC(11601240)

摘要/Abstract

摘要：

该文研究了一类耦合Korteweg-de Vries（KdV）方程组中两个仅依赖空间变量的输运系数的反演问题.为证明在单个内部测量数据下反问题的稳定性，该文先证明了该耦合KdV方程组的一个仅含单个局部积分项的卡勒曼估计，然后进一步得到了在先验信息下的反问题的Lipschitz稳定性.

关键词: 卡勒曼估计, 耦合KdV方程组, Lipschitz稳定性, 系数反问题

Abstract:

This paper concerns an inverse problem of determining two spatially varying transport coefficients simultaneously in a linearly coupled Korteweg-de Vries (KdV) system with the first order terms. To obtain the stability result for the inverse problem with only one internal measurement data, we first prove a Carleman estimate including only one local integral for this coupled KdV system. Based on this Carleman estimate, we then obtain Lipschitz stability for the inverse problem under some priori information.

Key words: Carleman estimate, Coupled KdV system, Lipschitz stability, Coefficient inverse problem

中图分类号:

O175.28

吴斌,陈群. 一类耦合Korteweg-de Vries方程组输运系数反演问题的Lipschitz稳定性[J]. 数学物理学报, 2021, 41(3): 740-761.

Bin Wu,Qun Chen. Lipschitz Stability for a Transport Coefficient Inverse Problem of a Linearly Coupled Korteweg-de Vries System[J]. Acta mathematica scientia,Series A, 2021, 41(3): 740-761.

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