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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2405.20637 |
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| _version_ | 1866914949104664576 |
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| author | Zhang, Zhiguang Li, Yuxxiang |
| author_facet | Zhang, Zhiguang Li, Yuxxiang |
| contents | In this work, we study the no-flux initial-boundary value problem for the doubly degenerate nutrient taxis system \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u v \nabla u)-χ\nabla \cdot\left(u^{2} v \nabla v\right)+\ell u v, & x \in Ω, t>0, \\ v_t=Δv-u v, & x \in Ω, t>0 \end{cases} \end{align} in a smoothly bounded convex domain $Ω\subset \mathbb{R}^2$, where $χ>0$ and $\ell \geq 0$. In this paper, we present that for all reasonably regular initial data, the model \eqref{eq 0.1} possesses a global bounded weak solution which is continuous in its first and essentially smooth in its second component. \end{abstract} |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness in a two-dimensional doubly degenerate nutrient taxis system Zhang, Zhiguang Li, Yuxxiang Analysis of PDEs In this work, we study the no-flux initial-boundary value problem for the doubly degenerate nutrient taxis system \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u v \nabla u)-χ\nabla \cdot\left(u^{2} v \nabla v\right)+\ell u v, & x \in Ω, t>0, \\ v_t=Δv-u v, & x \in Ω, t>0 \end{cases} \end{align} in a smoothly bounded convex domain $Ω\subset \mathbb{R}^2$, where $χ>0$ and $\ell \geq 0$. In this paper, we present that for all reasonably regular initial data, the model \eqref{eq 0.1} possesses a global bounded weak solution which is continuous in its first and essentially smooth in its second component. \end{abstract} |
| title | Boundedness in a two-dimensional doubly degenerate nutrient taxis system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.20637 |