论文标题
三维触觉交叉扩散系统建模溶瘤病毒疗法的渐近行为
Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy
论文作者
论文摘要
本文讨论了由溶瘤病毒疗法\ Begin \ begin {equation*} \ left \ \ \ {array} {lll} {lll} u_t =δu-\ nabla \ nabla \ cdot \ cdot（u \ cdot（u \ cd）+\ nabla v）+u（1） v_t = - （u+w）v，\\ w_t =Δw-\ nabla \ cdot（w \ nabla v）-w+uz，\\ z_t =d_zΔz-z-z-z-uz+βW， \ end {array} \ right。 \ end {equation*}在平稳界限域中$ω\ subset \ mathbb {r}^3 $带有$β> 0 $，〜$μ> 0 $和$ d_z> 0 $。基于自图论点 据表明，在假设$β\ max \ {1，\ | U_0 \ | _ {l^{l^{\ infty}（ω）} \} <1+（1+ \ frac1 {\ frac1 {\ min_ {\ min_ {x \ inω}}}}} u_0（x）} u_0（x）} u _0（x）} unlobal strique strique $（U，V，W，Z）$用于某些类型的小数据$（U_0，V_0，W_0，Z_0）$。此外，$（u，v，w，z）$在全球范围内，并成倍地稳定在其空间上均匀的平衡 ％恒定平衡 $（1,0,0,0）$ as $ t \ rightarrow \ infty $。
This paper deals with an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy \begin{equation*} \left\{ \begin{array}{lll} u_t=Δu-\nabla \cdot(u\nabla v)+μu(1-u)-uz,\\ v_t=-(u+w)v,\\ w_t=Δw-\nabla \cdot(w\nabla v)-w+uz,\\ z_t=D_zΔz-z-uz+βw, \end{array} \right. \end{equation*} in a smoothly bounded domain $Ω\subset \mathbb{R}^3$ with $β>0$,~$μ>0$ and $D_z>0$. Based on a self-map argument, it is shown that under the assumption $β\max \{1,\|u_0\|_{L^{\infty}(Ω)}\}< 1+ (1+\frac1{\min_{x\in Ω}u_0(x)})^{-1}$, this problem possesses a uniquely determined global classical solution $(u,v,w,z)$ for certain type of small data $(u_0,v_0,w_0,z_0)$. Moreover, $(u,v,w,z)$ is globally bounded and exponentially stabilizes towards its spatially homogeneous equilibrium %constant equilibrium $(1,0,0,0)$ as $t\rightarrow \infty$.
