ANALYSIS OF A FREE BOUNDARY TUMOR MODEL WITH TIME-DEPENDENT IN THE PRESENCE OF INHIBITORS

This paper investigates a free boundary tumor model with timedependent in the presence of inhibitors. The model consists of two diffusion equations representing nutrients and inhibitors respectively, and an ordinary differential equation describing the radius of the tumor R(t). We know that angiogenesis is not a steady-state process, in general, it changes over time, so it is reasonable to assume that tumors stimulate angiogenesis at a rate proportional to alpha(t). We find the properties of the tumor radius R(t) is greatly tied to the properties of alpha(t). When alpha (t) is time-dependent, we prove that for any sufficiently small c(1): If alpha(t) remains uniformly bounded, then R(t) also remains uniformly bounded; If alpha(t) tends to zero as t ->infinity, so does the tumor radius R(t); If lim(t ->infinity) inf alpha (t) > 0, then lim(t ->infinity) inf R (t) > 0. Moreover, the global asymptotic stability of the steady-state solution is proved, and it is surprising to find that when u +v over bar is sufficiently small and lambda/mu u over bar < c(1) <= c(2), the solution will blow up.