| 一类带裂缝散射问题的边界积分方程方法 |
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| 引用本文： | 管毅,赵远英,张文林.一类带裂缝散射问题的边界积分方程方法[J].数学的实践与认识,2020(5):173-181. |
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| 作者姓名： | 管毅 赵远英 张文林 |
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| 作者单位： | 贵阳学院数学与信息科学学院;六盘水师范学院数学与信息工程学院 |
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| 基金项目： | 国家自然科学基金(11761016);2019年度贵阳市科技局贵阳学院科技专项资金(GYU-KYZ(2019-2020)PT06-09);贵州省教育厅自然科学基金(黔教合KY字[2017]260号,KY字[2018]387号);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]210号)。 |
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| 摘 要： | 声波的散射问题中,如果散射体由不可穿透障碍物和可穿透裂缝两部分组成,障碍物表面分别满足第一类和第三类边界条件,裂缝两边满足不同的第二类边界条件,通过位势理论,可以将此混合问题转化为边界积分方程,通过Fredholm算子理论可以得到这个边界积分方程解的存在性和唯一性,从而获得原问题解的存在和唯一性.
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| 关 键 词： | HELMHOLTZ方程 边界积分方程 裂缝 |
The Boundary Integral Method for the Scattering Problem with Cracks |
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| GUAN Yi,ZHAO Yuan-ying,ZHANG Wen-lin.The Boundary Integral Method for the Scattering Problem with Cracks[J].Mathematics in Practice and Theory,2020(5):173-181. |
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| Authors: | GUAN Yi ZHAO Yuan-ying ZHANG Wen-lin |
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| Institution: | (College of Mathematics and Information Science,Guiyang University,Guiyang 550005,China;Shool of Mathematics and Information Engnieering,Liupanshui Normal University,Liupanshui 553004,China) |
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| Abstract: | we consider a kind of scattering problem by a crackΓthat is buried in a bounded domain D,both sides of the crack are given different impedance boundary conditions,and Dirichlet and impedance boundary conditions are set on the boundary of D.The problem can be reformulated as a system of boundary of integral equations by potential theory.We establish the existence and uniqueness of the solution to the system by using the Fredholm theory. |
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| Keywords: | Helmholtz equation boundary integral equation Crack |
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