Body resonances for classical waves
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911930974732288 |
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| author | Mantile, Andrea Posilicano, Andrea |
| author_facet | Mantile, Andrea Posilicano, Andrea |
| contents | We provide a detailed study of the spectral properties of the linear operator $H(\varepsilon)=-(\varepsilon^{2}χ_{Ω_{\varepsilon}}+χ_{Ω^{c}_{\varepsilon}})Δ$ modeling, through the wave equation $(\partial_{tt}+H(\varepsilon))u=0$, the dynamics of acoustic waves in the presence of a small inhomogeneity of size $\varepsilon$ having high contrast $\varepsilon^{-2}$. In particular, we give precise results on the localization of the resonances of $H(\varepsilon)$ and their first-order $\varepsilon$-expansions; the latter are explicitly expressed in terms of the eigenvalues and eigenvectors of the Newton potential operator of the set $Ω$ whose rescaling of size $\varepsilon$ defines $Ω_{\varepsilon}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Body resonances for classical waves Mantile, Andrea Posilicano, Andrea Spectral Theory Mathematical Physics Analysis of PDEs We provide a detailed study of the spectral properties of the linear operator $H(\varepsilon)=-(\varepsilon^{2}χ_{Ω_{\varepsilon}}+χ_{Ω^{c}_{\varepsilon}})Δ$ modeling, through the wave equation $(\partial_{tt}+H(\varepsilon))u=0$, the dynamics of acoustic waves in the presence of a small inhomogeneity of size $\varepsilon$ having high contrast $\varepsilon^{-2}$. In particular, we give precise results on the localization of the resonances of $H(\varepsilon)$ and their first-order $\varepsilon$-expansions; the latter are explicitly expressed in terms of the eigenvalues and eigenvectors of the Newton potential operator of the set $Ω$ whose rescaling of size $\varepsilon$ defines $Ω_{\varepsilon}$. |
| title | Body resonances for classical waves |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2406.17130 |