2021/10/10 by Song, Huijuan, Huang, Qian, Wang, Zejia
#35B35 #35Q92 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.04688
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.