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On the behavior of resonant frequencies in the presence of small anisotropic imperfections. (English) Zbl 1432.35073

Summary: In this paper we provide a rigorous derivation of an asymptotic formulae for perturbations in the resonant frequencies of the two-(or three-) dimensional Laplacian operator under geometric variation of the domain. The asymptotic expansion is developed in the presence and with respect to size of the (anisotropic) imperfections of small shapes having constitutive parameters different from the background conductivity. The main feature of the method is to yield a robust procedure making it possible to recover information about the location, shape, and material properties of the anisotropic imperfections.

MSC:

35J25 Boundary value problems for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35P25 Scattering theory for PDEs
35Q35 PDEs in connection with fluid mechanics
35Q61 Maxwell equations
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