一类带有非奇异主部系数矩阵的2×2强耦合偏微分系统的卡勒曼估计及其反源问题

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 779-799.

一类带有非奇异主部系数矩阵的2×2强耦合偏微分系统的卡勒曼估计及其反源问题

吴斌¹, 高莹¹, 闫林¹, 余军²

1 南京信息工程大学数学与统计学院南京 210044;
2 佛蒙特大学数学与统计学系美国佛蒙特州伯灵顿市 VT05401

收稿日期:2016-12-12 修回日期:2017-10-22 出版日期:2018-08-26 发布日期:2018-08-26
作者简介:吴斌,E-mail:binwu@nuist.edu.cn
基金资助:
国家自然科学基金（11661004，11601240）

Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem

Wu Bin¹, Gao Ying¹, Yan Lin¹, Yu Jun²

1 School of Mathematics and Statistics, College of Science, Nanjing University of Information Science and Technology, Nanjing 210044;
2 Department of Mathematics and Statistics, The University of Vermont, Burlington VT 05401, United States

Received:2016-12-12 Revised:2017-10-22 Online:2018-08-26 Published:2018-08-26
Supported by:
Supported by the NSFC (11661004, 11601240)

摘要/Abstract

摘要： 该文研究了一类带有非奇异系数矩阵的2×2强耦合偏微分方程组的卡勒曼估计.文献[7]和[15]利用对角化的技巧将方程组解耦，证明了一个2×2强耦合双曲方程组的卡勒曼估计.不同于此，该文考虑将微分方程组的两个方程作为整体来建立逐点的卡勒曼，然后进一步得到了这类强耦合方程组的全局卡勒曼估计.最后，作为卡勒曼估计的应用，该文建立了一个反源问题的Hölder稳定性.

关键词: 卡勒曼估计, 强耦合系统, 反源问题, Hölder稳定性

Abstract: We study a Carleman estimate for a 2×2 strongly coupled partial differential system with nonsingular coefficient matrix of principal parts. Different from the method to prove Carleman estimate for a strongly coupled hyperbolic system as in[7] and[15], we first establish a pointwise Carleman estimate by considering two equations in the governing system as a whole rather than by using diagonalization of the system. Furthermore, we prove a global Carleman estimate for this kind of strongly coupled differential system. Finally, as an application, we establish a Hölder stability for an inverse problem of determining two source functions by the boundary observation data.

Key words: Carleman estimate, Strongly coupled system, Inverse source problem, Hölder stability

中图分类号:

O175.28

吴斌, 高莹, 闫林, 余军. 一类带有非奇异主部系数矩阵的2×2强耦合偏微分系统的卡勒曼估计及其反源问题[J]. 数学物理学报, 2018, 38(4): 779-799.

Wu Bin, Gao Ying, Yan Lin, Yu Jun. Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem[J]. Acta mathematica scientia,Series A, 2018, 38(4): 779-799.

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