论文标题
Logistic源在具有非线性零级相互作用的二维触觉系统中的衰减效果
Dampening effect of logistic source in a two-dimensional haptotaxis system with nonlinear zero-order interaction
论文作者
论文摘要
本文讨论了溶溶性病毒疗法模型\ begin {equation} \ begin {split} \ begin {cases}＆u_t =Δu-\ nabla \ cdot（u \ nabla v）-Uz +μu（1-u）（1- u（1-u） ΔW -w + uz，＆\\ [2ex]＆z_t =d_zΔz-z- z- z- uz +βW，＆\ end {cases} \ end {split {split} \ end {ext} \ end {equation}在有限的域$ $ω$ $ $ $ $ $ $ $ $ \ subset $ $ $ $ $ $ \ bbb $ \ bbb { $β$处方为正参数。 对于任何适当的常规初始数据，对于允许$μ= 0 $的更通用模型的相应均质的诺伊曼初始结合问题的经典解决方案的全球存在已在$ [$ y中得到验证。 tao $ \＆M。M. Winkler，J。微分方程$ \ Mathbf {268} $（2020），4973-4997 $] $。这项工作进一步表明，每当$μ> 0 $ $> 0 $时，上述方程式上述全球经典解决方案均匀界定；此外，如果$β<1 $，则解决方案$（u，v，w，z）$稳定在拓扑$ l^p（ω）\ times（l^\ infty（ω））中的恒定平衡$（1、0、0、0、0）$，并在较大的时间限制中任何$ p> 1 $。
This paper deals with the oncolytic virotherapy model \begin{equation}\begin{split} \begin{cases} &u_t = Δu - \nabla \cdot (u\nabla v)-uz +μu(1-u),& \\[2ex] &v_t = - (u+w)v,& \\[2ex] &w_t = D_w Δw - w + uz,& \\[2ex] &z_t = D_z Δz - z - uz + βw,& \end{cases} \end{split}\end{equation} in a bounded domain $Ω$ $\subset$ $\Bbb{R}^2$ with smooth boundary, where $μ$, $D_w$, $D_z$ and $β$ are prescribed positive parameters. For any given suitably regular initial data, the global existence of classical solution to the corresponding homogeneous Neumann initial-boundary problem for a more general model allowing $μ=0$ was previously verified in $[$Y. Tao $\&$ M. Winkler, J. Differential Equations $\mathbf{268}$ (2020), 4973-4997$]$. This work further shows that whenever $μ>0$, the above-mentioned global classical solution to the above equation is uniformly bounded; and moreover, if $β<1$, then the solution $(u, v, w, z)$ stabilizes to the constant equilibrium $(1, 0, 0, 0)$ in the topology $L^p(Ω)\times (L^\infty(Ω))^3$ with any $p>1$ in a large time limit.
