The direct and inverse scattering problems for partially coated obstacles (Q2774156)

In the first part of the paper the authors investigate a boundary integral equation method for mixed boundary value problems for the Helmholtz equation. Uniqueness and existence of \(H^1\)-solutions is shown by applying the Riesz-Fredholm theory to a system of boundary integral equations in a product of Sobolev spaces. The second part of the paper is devoted to the inverse scattering problem to determine the shape of the scattering object from the knowledge of the far field patterns for all incident plane waves. The linear sampling method is discussed and a number of numerical examples are presented.NEWLINENEWLINE Editorial remark: In the paper [\textit{P. Krutitskii}, Int. J. Appl. Math. Res. 2, No. 1, 40--43 (2013; Zbl 1254.35244)] it is mentioned that thisNEWLINEarticle contains an error.