Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media

Fioralba Cakoni (1) , Houssem Haddar (2) , Nicolas Chaulet (2)

1 Department of Mathematical Sciences
2 DeFI - Shape reconstruction and identification

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 3.

Mots clés: Asymptotic analysis; transmission eigenvalue problem; thin layers

Domaines: Analyse numérique [cs.NA]

Fioralba Cakoni, Houssem Haddar, Nicolas Chaulet. Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media. IMA Journal of Applied Mathematics, 2014, pp.36. ⟨10.1093/imamat/hxu045⟩. ⟨hal-01109975⟩