2020/08/20 by Song, Huijuan, Hu, Wentao, Wang, Zejia
#35B35 #35Q92 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.08770
This paper is concerned with a nonlinear free boundary problem modeling the growth of spherically symmetric tumors with angiogenesis, set with a Robin boundary condition. In which, both nonnecrotic tumors and necrotic tumors are taken into consideration. The well-posedness and asymptotic behavior of solutions are studied. It is shown that there exist two thresholds, denoted by σ and σ^*, on the surrounding nutrient concentration σ. If σ≤σ, then the considered problem admits no stationary solution and all evolutionary tumors will finally vanish, while if σ>σ, then it admits a unique stationary solution and all evolutionary tumors will converge to this dormant tumor; moreover, the dormant tumor is nonnecrotic if σσ^*. The connection and mutual transition between the nonnecrotic and necrotic phases are also given.