彭超权,李傲,郭军.部分边界可穿透的障碍物的正散射问题[J].中南民族大学学报自然科学版,2019,(3):476-480
部分边界可穿透的障碍物的正散射问题
Positive scattering problem of partial boundary penetrable obstacles
  
DOI:10.12130/znmdzk.20190328
中文关键词: 声波散射  部分可穿透障碍物  解的适定性
英文关键词: acoustic scattering  partially penetrable obstacle  well-posedness of solution
基金项目:国家自然科学基金资助项目(11801575);中央高校基本科研业务费专项资助项目(CZT18010)
作者单位
彭超权,李傲,郭军* 中南民族大学 数学与统计学学院,武汉 430074 
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中文摘要:
      考虑一个可穿透障碍物的声波散射问题,障碍物一部分边界可以穿透,另一部分边界不能穿透.入射波在障碍物外部引起散射波,通过可穿透的边界时,在障碍物内部引起透射波.利用单双层位势理论,将问题转化为相应的边界积分方程组,再根据Fredholm定理证明了积分方程组解的存在性和唯一性,从而得到散射问题解的适定性.
英文摘要:
      The problem of acoustic scattering from a penetrable obstacle is considered. One part of the boundary of the obstacle can be penetrated, and the other part can not be penetrated. The incident wave induces the scattered wave outside the obstacle, and when it passes through the penetrable boundary, it causes the transmission wave inside the obstacle. By using the single-layer and double-layer potential theory, the problem is transformed into a corresponding boundary integral system, and the existence and uniqueness of the solution of the integral system are proved according to Fredholm’s theorem, and the well-posedness of the solution to the scattering problem is obtained.
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