High-contrast random composites: homogenisation framework and new spectral phenomena
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929545189261312 |
|---|---|
| author | Cherdantsev, Mikhail Cherednichenko, Kirill Velčić, Igor |
| author_facet | Cherdantsev, Mikhail Cherednichenko, Kirill Velčić, Igor |
| contents | We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator. Under some lenient assumptions on the configuration of the random inclusions, we fully characterise the limit of the spectra of the high-contrast operators in question, which unlike in the periodic setting is shown to be different to the spectrum of the homogenised operator. Introducing a new notion of the relevant limiting spectrum, we describe the connection between these two sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_00395 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | High-contrast random composites: homogenisation framework and new spectral phenomena Cherdantsev, Mikhail Cherednichenko, Kirill Velčić, Igor Analysis of PDEs Spectral Theory 35B27, 35P99, 74A40 We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator. Under some lenient assumptions on the configuration of the random inclusions, we fully characterise the limit of the spectra of the high-contrast operators in question, which unlike in the periodic setting is shown to be different to the spectrum of the homogenised operator. Introducing a new notion of the relevant limiting spectrum, we describe the connection between these two sets. |
| title | High-contrast random composites: homogenisation framework and new spectral phenomena |
| topic | Analysis of PDEs Spectral Theory 35B27, 35P99, 74A40 |
| url | https://arxiv.org/abs/2110.00395 |