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- W2475431347 abstract "We consider a family ${Omega^varepsilon}_{varepsilon>0}$ of periodic domains in $mathbb{R}^2$ with waveguide geometry and analyse spectral properties of the Neumann Laplacian $-Delta_{Omega^varepsilon}$ on $Omega^varepsilon$. The waveguide $Omega^varepsilon$ is a union of a thin straight strip of the width $varepsilon$ and a family of small protuberances with the so-called room-and-passage geometry. The protuberances are attached periodically, with a period $varepsilon$, along the strip upper boundary. For $varepsilonto 0$ we prove a (kind of) resolvent convergence of $-Delta_{Omega^varepsilon}$ to a certain ordinary differential operator. Also we demonstrate Hausdorff convergence of the spectrum. In particular, we conclude that if the sizes of passages are appropriately scaled the first spectral gap of $-Delta_{Omega^varepsilon}$ is determined exclusively by geometric properties of the protuberances. The proofs are carried out using methods of homogenization theory." @default.
- W2475431347 created "2016-08-23" @default.
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- W2475431347 date "2016-08-01" @default.
- W2475431347 modified "2023-09-27" @default.
- W2475431347 title "Spectrum of a singularly perturbed periodic thin waveguide" @default.
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