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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.12213 |
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| _version_ | 1866910623877562368 |
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| author | Burazin, Krešimir Erceg, Marko Waurick, Marcus |
| author_facet | Burazin, Krešimir Erceg, Marko Waurick, Marcus |
| contents | We prove a compactness result related to $G$-convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work related to applications, we do not require any boundedness or regularity of the underlying spatial domain; nor do we assume any periodicity or ergodicity assumption on the potentially oscillatory part. In terms of abstract evolutionary equations, we remove any compactness assumptions of the resolvent modulo kernel of the spatial operator. To achieve the results, we introduced a slightly more general class of material laws. As a by-product, we also provide a criterion for $G$-convergence for time-dependent equations solely in terms of static equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12213 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Evolutionary Equations are $G$-compact Burazin, Krešimir Erceg, Marko Waurick, Marcus Analysis of PDEs Mathematical Physics Functional Analysis Primary 35B27 Secondary 78M40, 80M40, 47D06 We prove a compactness result related to $G$-convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work related to applications, we do not require any boundedness or regularity of the underlying spatial domain; nor do we assume any periodicity or ergodicity assumption on the potentially oscillatory part. In terms of abstract evolutionary equations, we remove any compactness assumptions of the resolvent modulo kernel of the spatial operator. To achieve the results, we introduced a slightly more general class of material laws. As a by-product, we also provide a criterion for $G$-convergence for time-dependent equations solely in terms of static equations. |
| title | Evolutionary Equations are $G$-compact |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Primary 35B27 Secondary 78M40, 80M40, 47D06 |
| url | https://arxiv.org/abs/2311.12213 |