High-contrast random systems of PDEs: homogenisation and spectral theory
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929681140285440 |
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| author | Capoferri, Matteo Cherdantsev, Mikhail Velčić, Igor |
| author_facet | Capoferri, Matteo Cherdantsev, Mikhail Velčić, Igor |
| contents | We develop a qualitative homogenisation and spectral theory for elliptic systems of partial differential equations in divergence form with highly contrasting (i.e., non uniformly elliptic) random coefficients. The focus of the paper is on the behaviour of the spectrum as the heterogeneity parameter tends to zero; in particular, we show that in general one doesn't have Hausdorff convergence of spectra. The theoretical analysis is complemented by several explicit examples, showcasing the wider range of applications and physical effects of systems with random coefficients, when compared with systems with periodic coefficients or with scalar operators (both random and periodic). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09046 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High-contrast random systems of PDEs: homogenisation and spectral theory Capoferri, Matteo Cherdantsev, Mikhail Velčić, Igor Analysis of PDEs Mathematical Physics Spectral Theory primary 74S25, 74A40, secondary 35B27, 74Q15, 35B40, 60H15, 35P05 We develop a qualitative homogenisation and spectral theory for elliptic systems of partial differential equations in divergence form with highly contrasting (i.e., non uniformly elliptic) random coefficients. The focus of the paper is on the behaviour of the spectrum as the heterogeneity parameter tends to zero; in particular, we show that in general one doesn't have Hausdorff convergence of spectra. The theoretical analysis is complemented by several explicit examples, showcasing the wider range of applications and physical effects of systems with random coefficients, when compared with systems with periodic coefficients or with scalar operators (both random and periodic). |
| title | High-contrast random systems of PDEs: homogenisation and spectral theory |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory primary 74S25, 74A40, secondary 35B27, 74Q15, 35B40, 60H15, 35P05 |
| url | https://arxiv.org/abs/2312.09046 |