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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/2302.13868 |
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| _version_ | 1866910411416141824 |
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| author | Alves, Nuno J. Paulos, João |
| author_facet | Alves, Nuno J. Paulos, João |
| contents | In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the preservation of convergence under composition is investigated. The origin of this mode of convergence lies in the path of proving that the density of a Euler system converges almost everywhere (up to subsequences) towards the density of a non-linear diffusion system, as a consequence of the convergence in the relaxation limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A mode of convergence arising in diffusive relaxation Alves, Nuno J. Paulos, João Classical Analysis and ODEs Analysis of PDEs 28A20, 35Q35 In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the preservation of convergence under composition is investigated. The origin of this mode of convergence lies in the path of proving that the density of a Euler system converges almost everywhere (up to subsequences) towards the density of a non-linear diffusion system, as a consequence of the convergence in the relaxation limit. |
| title | A mode of convergence arising in diffusive relaxation |
| topic | Classical Analysis and ODEs Analysis of PDEs 28A20, 35Q35 |
| url | https://arxiv.org/abs/2302.13868 |