Global boundedness and finite time blow-up of solutions for a quasilinear chemotaxis-May-Nowak model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909558391177216 |
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| author | Wang, Jianping Wang, Mingxin |
| author_facet | Wang, Jianping Wang, Mingxin |
| contents | In this paper, we introduce the nonlinear diffusion term $\nabla\cdot(D(u)\nabla u)$ into the chemotaxis-May-Nowak model to investigate the effects of $D(u)$ and chemotaxis on the global existence, boundedness, and finite time blow-up of solutions. Here, $D(u)$ generalizes the prototype $(1+u)^{m-1}$ with $m\in\R$. For the parabolic-elliptic-parabolic case, if $m>2+\frac{n}{2}-\frac2{n}$ when $n\ge3$ and $m>\frac32$ when $n=2$, then all solutions exist globally and remain bounded, whereas if $n\in\{2,3\}$ and $m<1$, finite time blow-up occurs when $Ω$ is a ball and the initial data are radially symmetric. For the fully parabolic case, if $m>1+\frac{n}{2}-\frac2{n}$, then all solutions exist globally and remain bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global boundedness and finite time blow-up of solutions for a quasilinear chemotaxis-May-Nowak model Wang, Jianping Wang, Mingxin Analysis of PDEs In this paper, we introduce the nonlinear diffusion term $\nabla\cdot(D(u)\nabla u)$ into the chemotaxis-May-Nowak model to investigate the effects of $D(u)$ and chemotaxis on the global existence, boundedness, and finite time blow-up of solutions. Here, $D(u)$ generalizes the prototype $(1+u)^{m-1}$ with $m\in\R$. For the parabolic-elliptic-parabolic case, if $m>2+\frac{n}{2}-\frac2{n}$ when $n\ge3$ and $m>\frac32$ when $n=2$, then all solutions exist globally and remain bounded, whereas if $n\in\{2,3\}$ and $m<1$, finite time blow-up occurs when $Ω$ is a ball and the initial data are radially symmetric. For the fully parabolic case, if $m>1+\frac{n}{2}-\frac2{n}$, then all solutions exist globally and remain bounded. |
| title | Global boundedness and finite time blow-up of solutions for a quasilinear chemotaxis-May-Nowak model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.23645 |