期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

具有混合裂缝散射问题的边界积分方程方法 被引量：5

Integral Equations to the Scattering Problem by a Mixed Crack
下载PDF
导出
摘要 如果散射物体是一个无限长的部分圆柱体,该文讨论在时间调和的情况下,电磁波的散射问题.该散射体的水平截面是一条裂缝,那么,最终可以考虑在平面上,关于一条裂缝的混合边值问题.在平面上,这条裂缝就是一段弧.假设该弧光滑,而且被分成了两个部分,在每一部分,弧的两边具有不同的边界条件.应用位势理论,可以把该混合边值问题转化成一个边界积分方程组.通过分析该边界积分方程组中相应积分算子的性质,利用Fredholm定理,可以得到这个边界积分方程组解的存在与唯一性,从而获得原来问题解的存在与唯一性. Consider the scattering of an electro-magnetic time-harmonic plane wave by an infinite cylinder having a mixed open crack in R2 as the cross section. We assume that the crack is made of two parts, and one of which is （possibly） coated on one side by a material with surface impedance A. The problem can be reformulated as a boundary integral system （BIS） by using potential theory. We obtain the existence and uniqueness of the weak solution to the system by the Fredholm theory.
作者 严国政
机构地区 华中师范大学数学与统计学学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2011年第5期1167-1175,共9页 Acta Mathematica Scientia
基金 国家自然科学基金(10871080) 华中师范大学非线性分析实验室 湖北省数学物理重点实验室和教育部重点科技项目基金(107081)资助
关键词 裂缝散射 边界积分方程 Helmholtz方程. Scattering by crack Boundary integral equation Helmholtz equation.
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献20

  • 1Ammari H, Bao Gang, Wood A W. An integral equation method for the electromagnetic scattering from cavitys. Math Meth Appl Sci, 2000, 23:1057 -1072.
  • 2Cheng J, Hon Y C, Yamamoto M. Conditional stability estimations for a inverse boundary problem with non-smooth boundary in R3. Trans American Math Soc, 2001, 353:4123-4138.
  • 3Colton D L, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer, 1998.
  • 4Colton D L, Kress R. Integral Equation Methods in Scattering Theory. New York: Springer-Verlag, Wiley, 1983.
  • 5Costabel M. Boundary integral operator on Lipschitz domains: elementary results. SIAM J Math Anal, 1988, 19:613-626.
  • 6Cakoni F, Colton D L, Peter Monk. The direct and inverse scattering problems for partially coated obstacles. Inverse Problems, 2001, 1T: 1997-2015.
  • 7Cakoni F, Colton D L. The linear sampling method for cracks. Inverse Problems, 2003, 19:279-295.
  • 8Cakoni F, Colton D L. Qualitative Methods in Inverse Scattering Theory. Series on Interaction of Mathematics and Mechanics. Berlin, Heidelberg: Springer, 2006.
  • 9Hsiao G, Wolfgang L W. Boundary Integral Equations. Applied Mathematical Sciences 164. Berlin: Springer, 2008.
  • 10Ikehata M. Reconstruction of the shape of the inclusion by boundary measurments. Commun Partial Diff Eq, 1998, 23:1459-1474.

同被引文献34

  • 1CHEN Xin-fu, Friedman A. Maxwell's Equations in a Periodic Structure [J]. Trans Amer Math Soc, 1991, 323(2): 465-507.
  • 2Friedman A. Mathematics in Industrial Problems [M]. Part 3. Heidelberg: Springer-Verlag, 1990.
  • 3Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory [M]. Berlin: Springer, 1992: 1-199.
  • 4Dobson D, Friedman A. The Time Harmonic Maxwell Equations in a Doubly Periodic Structure [J]. Journal of Mathematical Analysis and Applications, 1992, 166(2) : 507-528.
  • 5Kress R. Inverse scattering from an open arc [J]. Math. Methods Appl. Sci., 1995,18(26):267-293.
  • 6Monch L. On the inverse acoustic scattering problem by an open arc: on the sound-hard case [J]. Inverse Problems, 1997,17(13): 1379-1392.
  • 7Cloton D, Kress R. Inverse acoustic and electromagnetic scattering theory [J].Inverse Problems, 2003,47(15) 68-109.
  • 8Cloton D, Kress R. Intergral Equation Methodsin Scattering Theory [M]. New York: Wiley Springer Verlag 1993.
  • 9Kress R. Inverse scattering from an open arc [ J ]. Mathe- matical Methods in the Applied Sciences, 1995,18 (4) : 267-293.
  • 10Monch L. On the numerical solution of the direct scattering problem for an open sound-hard arc [ J ]. Journal of Com- putational and Applied Mathematics, 1996,71 ( 2 ) : 343- 356.

引证文献5

二级引证文献7

数学物理学报（A辑）
2011年 第5期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部