Analysis of a nonlinear necrotic tumor model with angiogenesis and a periodic supply of external nutrients

Abstract

In this paper, we consider a free boundary problem modeling the growth of spherically symmetric necrotic tumors with angiogenesis and a ω-periodic supply φ(t) of external nutrients. In the model, the consumption rate of the nutrient and the proliferation rate of tumor cells S(σ) are both general nonlinear functions. The well-posedness and asymptotic behavior of solutions are studied. We show that if the average of S(φ(t)) is nonpositive, then all evolutionary tumors will finally vanish; the converse is also ture. If instead the average of S(φ(t)) is positive, then there exists a unique positive periodic solution and all other evolutionary tumors will converge to this periodic state.