讲座内容摘要：

In this paper, we consider a free boundary problem modeling the growth of tumor cord with time delay, in which the cell location is incorporated. This problem contains two partial differential equations and one ordinary differential equation defined in a bounded domain in $\mathbb{R}^2$, whose boundary includes two disjoint closed curves, one fixed and the other moving with a priori unknown. It is shown that there exists a unique radially symmetric stationary solution $(\sigma_\ast,p_\ast,R_\ast)$ when nutrient sufficient and small time delay. Moreover, under non-radially symmetric perturbations, the stationary solution $(\sigma_\ast,p_\ast,R_\ast)$ is linearly stable. The results indicate that adding the time delay in the model leads to a larger stationary tumor, and if the tumor aggressiveness is larger, the time delay has a greater impact on the size of tumor.