Analysis of a nonlinear free-boundary tumor model with angiogenesis and a connection between the nonnecrotic and necrotic phases

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.