qualitative analysis of a delayed free boundary problem for tumor growth under the effect of inhibitors

in this paper we study a delayed free boundary problem for the growth of tumors under the effect of inhibitors. the establishing of the model is based on the diffusion of nutrient and inhibitors, and mass conservation for the two processes proliferation and apoptosis. it is assumed that the process of proliferation is delayed compared to apoptosis. we mainly study the asymptotic behavior of the solution, and prove that under some assumptions, in the case where c₁ and c₂ are sufficiently small, the volume of the tumor cannot expand without limit; it will either disappear or evolve to a dormant state as t→∞.