zbMATH — the first resource for mathematics

The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation. (English) Zbl 0869.35068
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.DiblĂ­k (Brno)

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
Full Text: DOI