A spectral problem for the Laplacian in joined thin films

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URI: https://hdl.handle.net/10902/31588
ISSN: 0944-2669
ISSN: 1432-0835
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Autoría
Gaudiello, Antonio; Gómez Gandarillas, DelfinaAutoridad Unican; Pérez Martínez, María EugeniaAutoridad Unican
Fecha
2023-05
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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Calculus of Variations and Partial Differential Equations, 2023, 62(4), 129
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Springer Nature
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Resumen/Abstract
We consider a 3d multi-structure composed of two joined perpendicular thin films: a vertical one with small thickness han and a horizontal one with small thickness hbn. We study the asymptotic behavior, as han and hbntend 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 = limnhbnhan. 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.
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.