Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910907777417216 |
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| author | Fuest, Mario Lankeit, Johannes Mizukami, Masaaki |
| author_facet | Fuest, Mario Lankeit, Johannes Mizukami, Masaaki |
| contents | We consider the fully parabolic, spatially heterogeneous chemotaxis-growth system \begin{align*}
\begin{cases}
u_t = Δu - \nabla\cdot(u\nabla v) + κ(x)u-μ(x)u^2, \\
v_t = Δv - v + u
\end{cases} \end{align*} in bounded domains $Ω\subset \mathbb{R}^2$ and show that the blow-up set is contained in the set of zeroes of $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source Fuest, Mario Lankeit, Johannes Mizukami, Masaaki Analysis of PDEs 35B44, 35K55, 92C17 We consider the fully parabolic, spatially heterogeneous chemotaxis-growth system \begin{align*} \begin{cases} u_t = Δu - \nabla\cdot(u\nabla v) + κ(x)u-μ(x)u^2, \\ v_t = Δv - v + u \end{cases} \end{align*} in bounded domains $Ω\subset \mathbb{R}^2$ and show that the blow-up set is contained in the set of zeroes of $μ$. |
| title | Location of blow-up points in fully parabolic chemotaxis systems with spatially heterogeneous logistic source |
| topic | Analysis of PDEs 35B44, 35K55, 92C17 |
| url | https://arxiv.org/abs/2406.11746 |