Spectral properties of operators and wave propagation in high-contrast media
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917152785694720 |
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| author | Godin, Yuri A. Koralov, Leonid Vainberg, Boris |
| author_facet | Godin, Yuri A. Koralov, Leonid Vainberg, Boris |
| contents | The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media. A unified approach to solving problems in bounded domains with Dirichlet or Neumann boundary conditions, as well as in infinite periodic media, is proposed. For a small parameter $\varepsilon > 0$ characterizing the contrast of the components of the medium, the analyticity of the eigenvalues and eigenfunctions is established in a neighborhood of $\varepsilon = 0$. Effective operators corresponding to $\varepsilon = 0$ are described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral properties of operators and wave propagation in high-contrast media Godin, Yuri A. Koralov, Leonid Vainberg, Boris Analysis of PDEs Mathematical Physics The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media. A unified approach to solving problems in bounded domains with Dirichlet or Neumann boundary conditions, as well as in infinite periodic media, is proposed. For a small parameter $\varepsilon > 0$ characterizing the contrast of the components of the medium, the analyticity of the eigenvalues and eigenfunctions is established in a neighborhood of $\varepsilon = 0$. Effective operators corresponding to $\varepsilon = 0$ are described. |
| title | Spectral properties of operators and wave propagation in high-contrast media |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2504.10629 |