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A spectral problem for the Laplacian in joined thin films

Abstract: We consider a 3d multi-structure composed of two joined perpendicular thin films: a vertical one with small thickness hna and a horizontal one with small thickness hnb. We study the asymptotic behavior, as hna and hnb tend to zero, of an eigenvalue problem for the Laplacian defined on this multi-structure. We shall prove that the limit problem depends on the value q=limnhnbhna. Precisely, we pinpoint three different limit regimes according to q belonging to] 0 , + ?[, q equal to + ?, or q equal to 0. We identify the limit problems and we also obtain H1-strong convergence results.

 Fuente: Calculus of Variations and Partial Differential Equations, 2023, 62(4), 129

 Editorial: Springer Nature

 Fecha de publicación: 01/05/2023

 Nº de páginas: 31

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00526-023-02464-z

 ISSN: 0944-2669,1432-0835

 Proyecto español: PGC2018-098178-B-I00

 Url de la publicación: https://doi.org/10.1007/s00526-023-02464-z