The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation.

*(English)*Zbl 0869.35068A 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)

##### 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 |