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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.07201 |
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| _version_ | 1866929381801197568 |
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| author | Bai, Xueli Zhou, Maolin |
| author_facet | Bai, Xueli Zhou, Maolin |
| contents | In this paper, we obtain the exact blow-up profiles of solutions of the Keller-Segel-Patlak system in the space with dimensions $N\ge 3$, which solves an open problem proposed by P. Souplet and M. Winkler in 2019. To establish this achievement, we develop the zero number argument for nonlinear equations with unbounded coefficients and construct a family of auxiliary backward self-similar solutions through nontrivial ODE analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $N\ge 3$ Bai, Xueli Zhou, Maolin Analysis of PDEs In this paper, we obtain the exact blow-up profiles of solutions of the Keller-Segel-Patlak system in the space with dimensions $N\ge 3$, which solves an open problem proposed by P. Souplet and M. Winkler in 2019. To establish this achievement, we develop the zero number argument for nonlinear equations with unbounded coefficients and construct a family of auxiliary backward self-similar solutions through nontrivial ODE analysis. |
| title | Exact blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $N\ge 3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.07201 |