Existence and uniqueness of solutions for acoustic scattering over infinite obstacles

The paper considers the solution of the boundary value problem (BVP) consisting of the Helmholtz equation in the region D with a rigid boundary condition on ∂D and its reformulation as a boundary integral equation (BIE), over an infinite cylindrical surface of arbitrary smooth cross-section. A boundary integral equation, which models threedimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution of the integral equation and the corresponding boundary value problem.