Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary

Klas Pettersson

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arXiv · 2004.07023

Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary

Klas Pettersson

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Abstract

We study a Dirichlet spectral problem for a second-order elliptic operator with locally periodic coefficients in a thin domain. The boundary of the domain is assumed to be locally periodic. When the thickness of the domain $\varepsilon$ tends to zero, the eigenvalues are of order $\varepsilon^{-2}$ and described in terms of the first eigenvalue $\mu(x_1)$ of an auxiliary spectral cell problem parametrized by $x_1$, while the eigenfunctions localize with rate $\sqrt{\varepsilon}$.

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Klas Pettersson. 2020-04-15. Localization of eigenfunctions in a thin domain with locally periodic oscillating boundary. https://arxiv.org/abs/2004.07023

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