The boundary integral method for the Helmholtz equation with cracks inside a bounded domain. Issue 3 (May 2015)

• Record Type: Journal Article
• Authors: GUO, Jun; FAN, Lili; YAN, Guozheng
• Is Part Of: Acta mathematica scientia. Volume 35:Issue 3(2015)
• Page Start: 539
• Page End: 551
• Publication Date: 2015-05
• Subjects: Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(15)30002-3
• Languages: English
• ISSNs: 0252-9602

Abstract

<abstract abstract-type="author" id="ceab10"> <title id="cestitle10">Abstract</title> <sec> <p id="spara10">We consider a kind of scattering problem by a crack Γ that is buried in a bounded domain <italic>D</italic>, and we put a point source inside the domain <italic>D</italic>. This leads to a mixed boundary value problem to the Helmholtz equation in the domain <italic>D</italic> with a crack Γ. Both sides of the crack Γ are given Dirichlet-impedance boundary conditions, and different boundary condition (Dirichlet, Neumann or Impedance boundary condition) is set on the boundary of <italic>D</italic>. Applying potential theory, the problem can be reformulated as a system of boundary integral equations. We establish the existence and uniqueness of the solution to the system by using the Fredholm theory.</p> </sec> </abstract>