基于交互间隙法的内部混合边界条件反散射问题  

Reciprocity Gap Method for an Interior Inverse Scattering Problem with a Mixed Boundary Condition

作　　者：汪晓青 刘立汉 吴雪娇 WANG Xiaoqing;LIU Lihan;WU Xuejiao(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：《重庆师范大学学报（自然科学版）》2023年第3期106-113,共8页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金青年项目(No.12001075);重庆市自然科学基金面上项目(No.cstc2020jcyj-msxmX0167);重庆市教育委员会科学技术研究项目(No.KJZD-K202100503,No.KJQN201900544);重庆市留学人员回国创新类项目(No.cx2021061,No.cx2019022);重庆师范大学青年拔尖人才培育计划(No.02030307/0052);重庆市巴渝学者计划(No.BYQNCS2020002);重庆市高校创新研究群体项目(No.CXQT20014)。

摘　　要：【目的】内部混合边界条件反散射问题在无损探测等方面有着广泛的应用。【方法】从位于腔体内部封闭曲线上点源产生的散射波出发,基于交互间隙法,构造交互间隙泛函,根据交互间隙泛函的范数性质来确定腔体的位置和形状。【结果】证明了内部混合边界条件反问题的唯一性和交互间隙泛函是单射且稠密的。【结论】由内部点源测量数据可以唯一确定未知腔体的位置、形状和阻抗函数。[Purposes]The interior inverse scattering problem with a mixed boundary condition is widely used in nondestructive detection.[Methods]From the scattered wave generated by the point source located on the closed curve inside the cavity,the reciprocity gap functional is constructed based on the reciprocity gap method,the position and shape of the cavity are determined according to the norm property of the interaction gap functional.[Results]It is proved that the solution of interior inverse problem with a mixed boundary condition is unique and the reciprocity gap functional is injective and dense.[Conclusions]The position,shape and boundary impedance function of unknown cavity can be uniquely determined from the measurement data.

关 键 词：交互间隙法 内部反散射问题 混合边界条件 阻抗函数 

分 类 号：O221.6[理学—运筹学与控制论]