Upper bounds for the blow-up time of the 2-D parabolic-elliptic Patlak-Keller-Segel model of chemotaxis
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910907110522880 |
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| author | Maheux, Patrick |
| author_facet | Maheux, Patrick |
| contents | In this paper, we obtain upper bounds for the critical time $T^*$ of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the mass is assumed. The result is expressed not only in terms of the supercritical mass $M> 8π$, but also in terms of the {\it shape} of the initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07076 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Upper bounds for the blow-up time of the 2-D parabolic-elliptic Patlak-Keller-Segel model of chemotaxis Maheux, Patrick Analysis of PDEs 35Q92, 35B44, 35K55, 35M31, 92C17 In this paper, we obtain upper bounds for the critical time $T^*$ of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the mass is assumed. The result is expressed not only in terms of the supercritical mass $M> 8π$, but also in terms of the {\it shape} of the initial data. |
| title | Upper bounds for the blow-up time of the 2-D parabolic-elliptic Patlak-Keller-Segel model of chemotaxis |
| topic | Analysis of PDEs 35Q92, 35B44, 35K55, 35M31, 92C17 |
| url | https://arxiv.org/abs/2306.07076 |