TY - JOUR KW - Transmission eigenvalues KW - Thin layers KW - Asymptotic methods KW - Inverse scattering TI - Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media UR - https://discovery.ucl.ac.uk/id/eprint/1414829/ AV - public JF - Journal of Applied Mathematics SN - 1110-757X N1 - Submitted ID - discovery1414829 A1 - Cakoni, F A1 - Chaulet, N A1 - Haddar, H Y1 - 2014/// N2 - We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max-Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order three. ER -