In this paper, we study a free boundary problem modeling the radial growth of a triple-layered tumor which is comprised of a central necrotic core and two annularly distributed living cell layers. Unlike necrotic cells never expending energy and nutrients, the living cells—quiescent cells and proliferating cells—consume externally supplied nutrients at clearly different rates. It is assumed that the linear consumption rate function by the living cells is increasing and jump discontinuous at a nutrient level \(\sigma _{Q}\) , which results from the biological observation that both living cells perform distinct cellular metabolic activity during the evolution. The jump discontinuity assumption is more realistic but brings much more difficulty in the rigorous analysis of the triple-layered tumor model, especially in the determination of the inner interfaces \({{\rho }}\) and \({{\eta }}\) between different cell layers and the study of their properties. Complete classification of tumor structures under different parameter conditions is provided. Two nutrient thresholds \(\sigma _{*}\) and \(\sigma ^{*}\) are obtained to distinguish the different steady states of the dormant tumor, which correspond to different types of stationary solutions. Based on this, we are able to completely depict the different dynamical behavior of tumor evolution corresponding to different transient solutions, under every parameter condition.
