Radially symmetric growth of necrotic tumors and connection with nonnecrotic tumors

Abstract

In this paper we study a nonlinear free boundary problem for radially symmetric growth of tumors with necrosis. We show this problem is globally well-posed and find a threshold value σ∗>0, such that if and only if external nutrient supply σ̄≥σ∗, there exists a unique necrotic stationary solution. We prove it is globally asymptotically stable. For σ̄<σ∗, asymptotic behavior of transient solution has been studied. The connection and mutual transition between necrotic and nonnecrotic tumors are also given.