Radially symmetric growth of necrotic tumors and connection with nonnecrotic tumors. (December 2019)

• Record Type: Journal Article
• Authors: Wu, Junde; Wang, Chen
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 25
• Page End: 33
• Publication Date: 2019-12
• Subjects: 35B35 -- 35B40 -- 35R35 -- 35Q92 -- 92C50; Free boundary problem -- Stationary solution -- Necrotic tumor -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.04.012
• Languages: English
• ISSNs: 1468-1218

Abstract

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 σ ̄ ≥ σ ∗, there exists a unique necrotic stationary solution. We prove it is globally asymptotically stable. For σ ̄ < σ ∗, asymptotic behavior of transient solution has been studied. The connection and mutual transition between necrotic and nonnecrotic tumors are also given.