Bendali, A.; Lemrabet, K. The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation. (English) Zbl 0869.35068 SIAM J. Appl. Math. 56, No. 6, 1664-1693 (1996). A model problem in the scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell is examined. In this paper, the contrast coefficients of the thin shell are assumed to remain finite. Such a treatment leads to a singular perturbation term that creates a typical difficulty for the asymptotic analysis of the problem with respect to the thickness of the coating. As a result, the asymptotic analysis is essentially based on a suitable handling of the stability of the solution relative to the thickness. As a consequence, it is shown how effective boundary conditions, which can be substituted to the thin shell, can then be obtained and analyzed in a simple way. Reviewer: J.Diblík (Brno) Cited in 59 Documents MSC: 35P25 Scattering theory for PDEs 78A40 Waves and radiation in optics and electromagnetic theory 35C20 Asymptotic expansions of solutions to PDEs 35B25 Singular perturbations in context of PDEs 78A45 Diffraction, scattering Keywords:scattering of a time-harmonic wave by an obstacle coated with a thin penetrable shell; asymptotic analysis; effective boundary conditions PDFBibTeX XMLCite \textit{A. Bendali} and \textit{K. Lemrabet}, SIAM J. Appl. Math. 56, No. 6, 1664--1693 (1996; Zbl 0869.35068) Full Text: DOI