Article
MSC:
35B40,
35J25,
35P05,
74B05,
74E10,
74G10 | MR 1981533 | Zbl 1022.74003 | DOI: 10.21136/MB.2002.134169
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Keywords:
spectral problem; thin domain; boundary layer; trapped mode; localized eigenfunction
spectral problem; thin domain; boundary layer; trapped mode; localized eigenfunction
Summary:
It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain $\Omega _h$ is localized either at the whole lateral surface $\Gamma _h$ of the domain, or at a point of $\Gamma _h$, while the eigenfunction decays exponentially inside $\Omega _h$. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and Neumann problems, too.
References:
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