This paper deals with an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy $$\left\{\begin{array}{c}{u}_t=\mathrm{\Delta }u-\nabla \cdot (u\nabla v)+\mu u(1-u)-uz,\hfill \\ v_t=-(u+w)v,\hfill \\ w_t=\mathrm{\Delta }w-\nabla \cdot (w\nabla v)-w+uz,\hfill \\ z_t=D_z\mathrm{\Delta }z-z-uz+\beta w,\hfill \end{array}\right.$$ in a smoothly bounded domain $\mathrm{\Omega }\subset {ℝ}^3$ with $\beta >0$, $\mu >0$ and $D_z>0$. Based on a self-map argument, it is shown that under the assumption $\beta max\{1,\parallel u_0{\parallel }_{L^{\infty }(\mathrm{\Omega })}\}<1+{(1+\frac{1}{{min}_{x\in \mathrm{\Omega }}{u}_0(x)})}^{-1}$, 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 toward its spatially homogeneous equilibrium $(1,0,0,0)$ as $t\to \infty$.

本文讨论了溶瘤病毒疗法产生的双触趋交叉扩散系统的初始边界值问题$$\left\{\begin{array}{c}{你}_t=\mathrm{\Delta }你-\nabla \cdot （你\nabla v）+\mu 你（1-你）-你z,\hfill \\ v_t=-（你+w）v,\hfill \\ w_t=\mathrm{\Delta }w-\nabla \cdot （w\nabla v）-w+你z,\hfill \\ z_t=D_z\mathrm{\Delta }z-z-你z+\beta w,\hfill \end{array}\right.$$在光滑有界域中$\mathrm{\Omega }\subset {ℝ}^3$和$\beta >0$,$\mu >0$和$D_z>0$。基于自映射论证，表明在假设下$\beta 最大限度\{1,\parallel {你}_0{\parallel }_{L^{\mathrm{无穷大}}（\mathrm{\Omega }）}\}<1+{（1+\frac{1}{{分钟}_{X\epsilon \mathrm{\Omega }}{你}_0（X）}）}^{-1}$，该问题拥有唯一确定的全局经典解$（你,v,w,z）$对于某些类型的小数据$（{你}_0,v_0,w_0,z_0）$。而且，$（你,v,w,z）$是全局有界的并且呈指数稳定地趋向其空间均匀平衡$（1,0,0,0）$作为$t\to \mathrm{无穷大}$。