| Autor: |
Gómez, Delfina, Nazarov, Sergei A., Orive-Illera, Rafael, Pérez-Martínez, Maria-Eugenia |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1002/mana.202100589 |
| Popis: |
In this paper, we provide uniform bounds for convergence rates of the low frequencies of a parametric family of problems for the Laplace operator posed on a rectangular perforated domain of the plane of height $H$. The perforations are periodically placed along the ordinate axis at a distance $O(\epsilon)$ between them, where $\epsilon$ is a parameter that converges towards zero. Another parameter $\eta$, the Floquet-parameter, ranges in the interval $[-\pi, \pi]$. The boundary conditions are quasi-periodicity conditions on the lateral sides of the rectangle and Neumann over the rest. We obtain precise bounds for convergence rates which are uniform on both parameters $\epsilon$ and $\eta$ and strongly depend on $H$. As a model problem associated with a waveguide, one of the main difficulties in our analysis comes near the nodes of the limit dispersion curves. |
| Databáze: |
arXiv |
| Externí odkaz: |
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