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

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

作　　者：吴斌[1] 陈群[1] Wu Bin;Chen Qun(School of Mathematics and Statistics,College of Science,Nanjing University of Information Science and Technology,Nanjing 210044)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《数学物理学报（A辑）》2021年第3期740-761,共22页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601240)。

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.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.

关 键 词：卡勒曼估计 耦合KDV方程组 LIPSCHITZ稳定性 系数反问题 

分 类 号：O175.28[理学—数学]