基于边界积分方程方法的可穿透非均匀介质反散射中的传输特征值问题  

A boundary integral equation method for transmission eigenvalue problems in penetrable inhomogeneous media

作　　者：郑秋燕 刘立汉 陈容 ZHENG Qiuyan;LIU Lihan;CHEN Rong(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《中山大学学报（自然科学版）（中英文）》2022年第3期181-188,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金青年科学基金(12001075);重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0167);重庆市教委科学技术研究项目(KJZD-K202100503,KJQN201900544);重庆市留学人员回国创新类项目(cx2021061,cx2019022);重庆市巴渝学者计划(BYQNCS2020002);重庆师范大学青年拔尖人才培育计划(02030307/0052);重庆市高校创新研究群体项目(CXQT20014)。

摘　　要：利用边界积分方程方法研究了可穿透非均匀介质反散射中的传输特征值问题。首先,根据可穿透非均匀介质反散射中传输特征值问题的特征,构造Robin-Dirichlet算子,并用边界积分算子表示Robin-Dirichlet算子。然后,由格林公式、Fredholm变换和迹定理,证明了一种算子的强制性。其次,应用紧嵌入定理和Lax-Milgram定理,证明了另一种算子的紧性。最后,结合两种算子的性质,证明了Robin-Dirichlet算子的差算子是指数为0的Fredholm算子且解析。The transmission eigenvalue problems in inverse scattering of penetrable inhomogeneous media is studied by using a boundary integral equation method.Firstly,the Robin-Dirichlet operator is constructed from the transmission eigenvalue problems in inverse scattering of penetrable inhomogeneous media,and the Robin-Dirichlet operator is represented by the boundary integral operator.Secondly,the coerciveness of an operator is proved by the Green's formula,Fredholm alternative and the trace the‐orem.Thirdly,the compact embedding theorem and Lax-Milgram theorem are applied to prove the compactness of another operator.Finally,combining the properties of the two operators,it is proved that the difference operator of the Robin-Dirichlet operator is an analytic Fredholm operator whose exponent is 0.

关 键 词：边界积分方程方法 传输特征值问题 Robin-Dirichlet算子 FREDHOLM算子 

分 类 号：O175[理学—数学]