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Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands

Abstract: We consider a Dirichlet spectral problem for a second order differential operator, with piecewise constant coefficients, in a domain in the plane . Here is , where ? is a fixed bounded domain with boundary ?, is a curvilinear band of width , and . The density and stiffness constants are of order and respectively in this band, while they are of order 1 in ?; , , and ? is a small positive parameter. We address the asymptotic behavior, as , for the eigenvalues and the corresponding eigenfunctions. In particular, we show certain localization effects for eigenfunctions associated with low frequencies. This is deeply involved with the extrema of the curvature of ?.

 Fuente: Journal of differential equations Volume 270, 5 January 2021, Pages 1160-1195

Editorial: Elsevier

 Fecha de publicación: 01/01/2021

Nº de páginas: 36

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jde.2020.09.011

ISSN: 1090-2732,0022-0396

Proyecto español: PGC2018-098178-B-I00

Url de la publicación: https://doi.org/10.1016/j.jde.2020.09.011