病毒动力学中具有逻辑阻尼的趋化-May-Nowak模型的全局有界性

中文摘要 AI 辅助

本文研究有界域 $\Omega \subset \mathbb{R}^n$（$n \ge 2$）中病毒感染的如下 May--Nowak 型模型：$\begin{cases} u_t = \Delta u - \chi \nabla \cdot (u \nabla v) + \kappa - u - uw - \mu \dfrac{u^{1+\alpha}}{\ln^k(u+e)}, \\\\[1mm] \gamma v_t = \Delta v - v + uw, \\\\[1mm] w_t = \Delta w - w + v, \end{cases}$ 其中 $\chi \in \mathbb{R}$，$\mu > 0$，$k \in [0,1)$，$\alpha > 0$，$\gamma \in \{0,1\}$。我们在以下条件之一成立时，对适当正则的初始数据建立了经典解的全局存在性和关于时间的一致有界性：（A）$\gamma = 1$，$n = 2$，$k \in [0,1)$，$\alpha = 1$，$\mu > 0$；（B）$\gamma = 1$，$3 \le n \le 5$，$k = 0$，$\alpha = 1$，且 $\mu$ 充分大；（C）$\gamma = 1$，$n \ge 6$，$k = 0$，$\alpha > \frac{n-2}{4}$，$\mu > 0$；（D）$\gamma = 0$，$n \ge 2$，$k = 0$，$\alpha > \frac{n+2}{2}$，$\mu>0$。特别地，在物理相关的维度 $n = 2,3$ 中，次二次和二次阻尼都足以防止爆破。此外，在全抛物情形（$\gamma = 1$）下，我们的结果改进了近期发现，将条件 $\alpha > \frac{n}{2}$ 在上述参数范围内放宽为更弱的假设。

英文摘要

This paper investigates the following May--Nowak type model for viral infection in a bounded domain $Ω\subset \mathbb{R}^n$, $n \ge 2$: $\begin{cases} u_t = Δu - χ\nabla \cdot (u \nabla v) + κ- u - uw - μ\dfrac{u^{1+α}}{\ln^k(u+e)}, \\[1mm] γv_t = Δv - v + uw, \\[1mm] w_t = Δw - w + v, \end{cases}$ where $χ\in \mathbb{R}$, $μ> 0$, $k \in [0,1)$, $α> 0$, and $γ\in \{0,1\}$. We establish the global existence and uniform-in-time boundedness of classical solutions for suitably regular initial data under one of the following conditions: (A) $γ= 1$, $n = 2$, $k \in [0,1)$, $α= 1$, and $μ> 0$; (B) $γ= 1$, $3 \le n \le 5$, $k = 0$, $α= 1$, and $μ$ is sufficiently large; (C) $γ= 1$, $n \ge 6$, $k = 0$, $α> \frac{n-2}{4}$, and $μ> 0$; (D) $γ= 0$, $n \ge 2$, $k = 0$, $α> \frac{n+2}{2}$, and $μ>0$. In particular, in the physically relevant dimensions $n = 2,3$, both subquadratic and quadratic damping are sufficient to prevent blow-up. Moreover, in the fully parabolic case ($γ= 1$), our results improve upon recent findings by relaxing the condition $α> \frac{n}{2}$ to weaker assumptions within the above parameter regimes.

发表机构

• Westlake University（西湖大学）

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