Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1167-1175.

• Articles • Previous Articles     Next Articles

Integral Equations to the Scattering Problem by a Mixed Crack

 YAN Guo-Zheng   

  1. Faculty of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079
  • Received:2009-07-05 Revised:2010-11-28 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    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

Abstract:

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 λ. 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.

Key words: Scattering by crack, Boundary integral equation, Helmholtz equation

CLC Number: 

  • 35D05
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