具有非光滑边界的散射问题  

Existence and uniqueness of solutions to scattering problem with non-smooth boundary

作　　者：黄军华[1] 

机构地区：[1]玉林师范学院数学与计算机科学系,广西玉林537000

出　　处：《华中师范大学学报（自然科学版）》2007年第1期8-10,15,共4页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(10471052)

摘　　要：讨论了一类具有非光滑边界的散射体的散射问题.为了简单起见,只针对R2空间.通过单双层位势,所讨论的问题可以化为一个边界积分方程.由于边界不光滑(有尖点),必须对边界积分算子进行仔细分析,最后得到了相应解的存在性和唯一性.This paper discusses the scattering problem with non-smooth boundary. For simplicity, the discussion will be restricted in R2 space. However the problem can be reformulated as a bounding integral equation by using the single, and double-layer potentials. The existence and uniqueness of the solution can be obtained by carefully analysis of the boundary integral operators（with singular point）.

关 键 词：散射问题 HELMHOLTZ方程 位势 

分 类 号：O175[理学—数学]