Finite-time blowup in a parabolic-parabolic-elliptic chemotaxis model involving indirect signal production
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918270076977152 |
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| author | Mao, Xuan Li, Yuxiang |
| author_facet | Mao, Xuan Li, Yuxiang |
| contents | This paper is concerned with a three-component chemotaxis model accounting for indirect signal production,reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$,$v_t = Δv - v + w$ and $0 = Δw - w + u$,posed in a ball of $\mathbb R^n$ with $n\geq5$,subject to homogeneous Neumann boundary conditions.The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88--148; 266 (2019), 942--976].We prove that for any prescribed mass $m > 0$, there exist radially symmetric and positive initial data $(u_0,v_0)\in C^0(\overlineΩ)\times C^2(\overlineΩ)$ with $\int_Ωu_0 = m$ such that the corresponding solutions blow up in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-time blowup in a parabolic-parabolic-elliptic chemotaxis model involving indirect signal production Mao, Xuan Li, Yuxiang Analysis of PDEs Primary 35B44, Secondary 35K51, 35Q92, 92C17 This paper is concerned with a three-component chemotaxis model accounting for indirect signal production,reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$,$v_t = Δv - v + w$ and $0 = Δw - w + u$,posed in a ball of $\mathbb R^n$ with $n\geq5$,subject to homogeneous Neumann boundary conditions.The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88--148; 266 (2019), 942--976].We prove that for any prescribed mass $m > 0$, there exist radially symmetric and positive initial data $(u_0,v_0)\in C^0(\overlineΩ)\times C^2(\overlineΩ)$ with $\int_Ωu_0 = m$ such that the corresponding solutions blow up in finite time. |
| title | Finite-time blowup in a parabolic-parabolic-elliptic chemotaxis model involving indirect signal production |
| topic | Analysis of PDEs Primary 35B44, Secondary 35K51, 35Q92, 92C17 |
| url | https://arxiv.org/abs/2412.10772 |