Asymptotique de valeurs propres de l'opérateur Poincaré-Neumann associé à deux inclusions proches

Abstract : In a composite medium that contains close-to-touching conducting inclusions, the pointwise values of the gradient of the voltage potential may blow up as the distance [delta] between some inclusions tends to 0 and as the conductivity contrast degenerates. We showed that the blow-up rate of the gradient is related to how the eigenvalues of the associated Neumann-Poincaré operator converge to +-1/2 as [delta] to 0, and on the regularity of the contact. Here, we consider two connected 2-D inclusions, at a distance [delta]>0 from each other. When [delta]=0, the contact beteween the inclusions is of order m>=2. We numerically determine the asymptotic behavior of the eigenvalues to the Neumann-Poincaré operator, in terms of [delta] and m.
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Master thesis
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Chun-Hsiang Tsou. Asymptotique de valeurs propres de l'opérateur Poincaré-Neumann associé à deux inclusions proches. Mathématiques [math]. 2014. ⟨hal-01841089⟩

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