Analysis of a nonlinear free-boundary tumor model with angiogenesis and a connection between the nonnecrotic and necrotic phases. (June 2021) - Song, Huijuan; Hu, Wentao; Wang, Zejia
Abstract: 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 σ ̃ < σ ̄ ≤ σ ∗ and necrotic if σ ̄ > σ ∗ . The connection and mutual transition between the nonnecrotic and necrotic phases are also given.