[1]管 毅,杨 媛,赵远英*.一类Helmholtz方程解的存在性和唯一性[J].四川师范大学学报(自然科学版),2018,(03):351-356.[doi:10.3969/j.issn.1001-8395.2018.03.013]
 GUAN Yi,YANG Yuan,ZHAO Yuanying.Existence and Uniqueness of a Solution to the Helmholtz Equation with Mixed Boundary Conditions[J].Journal of SichuanNormal University,2018,(03):351-356.[doi:10.3969/j.issn.1001-8395.2018.03.013]
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一类Helmholtz方程解的存在性和唯一性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
351-356
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Existence and Uniqueness of a Solution to the Helmholtz Equation with Mixed Boundary Conditions
文章编号:
1001-8395(2018)03-0351-06
作者:
管 毅 杨 媛 赵远英*
贵阳学院 数学与信息科学学院, 贵州 贵阳 550005
Author(s):
GUAN Yi YANG Yuan ZHAO Yuanying
College of Mathematics and Information Science, Guiyang University, Guiyang 550005, Guizhou
关键词:
Helmholtz 方程 边界积分方程 裂缝
Keywords:
Helmholtz equation boundary integral equation crack
分类号:
O175.23
DOI:
10.3969/j.issn.1001-8395.2018.03.013
文献标志码:
A
摘要:
声波的散射问题中,散射体由两部分组成:里面是一个不可穿透的障碍物,外面是一条可穿透的裂缝.不可穿透障碍物由两部分组成,不同部分的边界条件不同.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性和唯一性.
Abstract:
In the acoustic scattering problems, a scattering problem will occur when an incident wave meets an impenetrable obstacle after crossing a penetrable crack first. If the impenetrable obstacle consists of two parts, this will lead to two different boundary conditions. We can reformulate this problem as a boundary integral system by using potential theory. We obtain the existence and uniqueness of the weak solution to the system by using the fredholm theory.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-10-13 接受日期:2017-06-20
基金项目:国家自然科学基金(11761016)和贵州省科技厅联合基金(黔科合LH字[2014]7171号和黔科合LH字[2014]7176号)
*通信作者简介:赵远英(1981—),男,博士,主要从事应用数学与统计的研究,E-mail:zhaoyuanying@126.com
更新日期/Last Update: 2018-03-15