一类带有非奇异主部系数矩阵的2×2强耦合偏微分方程组的卡勒曼估计及其在反源问题中的应用  

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

作　　者：吴斌[1] 高莹 闫林 余军 Wu Bin;Gao Ying;Yan Lin;Yu Jun(School of Mathematics and Statistics,College of Science,Nanjing University of Information Science and Technology,Nanjing 210044;Department of Mathematics and Statistics,The University of Vermont,Burlington VT05401,United States)

机构地区：[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

出　　处：《数学物理学报（A辑）》2018年第4期779-799,共21页Acta Mathematica Scientia

基　　金：国家自然科学基金(11661004,11601240)。

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Hlder稳定性.We study a Carleman estimate for a 2x2 strongly coupled partial differential systemwith nonsingular coefficient matrix of principal parts.Different from the method to proveCarleman estimate for a strongly coupled hyperbolic system as in[7]and[15],we first establisha pointwise Carleman estimate by considering two equations in the governing system as a wholerather than by using diagonalization of the system.Furthermore,we prove a global Carlemanestimate for this kind of strongly coupled differential system.Finally,as an application,weestablish a H?lder stability for an inverse problem of determining two source functions by theboundary observation data.

关 键 词：卡勒曼估计 强耦合系统 反源问题 Holder稳定性 

分 类 号：O175.28[理学—数学]