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On the asymptotics of a Robin eigenvalue problem

Fioralba Cakoni 1 Nicolas Chaulet 2 Houssem Haddar 2
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : The considered Robin problem can formally be seen as a small perturbation of a Dirichlet problem. However, due to the sign of the impedance value, its associated eigenvalues converge point-wise to −∞ as the perturbation goes to zero. We prove in this case that Dirichlet eigenpairs are the only accumulation points of the Robin eigenpairs with normalized eigenvectors. We then provide a criterion to select accumulating sequences of eigenvalues and eigenvectors and exhibit their full asymptotic with respect to the small parameter.
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Submitted on : Thursday, November 21, 2013 - 10:41:36 AM
Last modification on : Friday, November 26, 2021 - 6:00:09 PM

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Fioralba Cakoni, Nicolas Chaulet, Houssem Haddar. On the asymptotics of a Robin eigenvalue problem. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2013, 351, pp.517-521. ⟨10.1016/j.crma.2013.07.022⟩. ⟨hal-00907355⟩



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