A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis. (June 2019)

• Record Type: Journal Article
• Authors: Shen, Haishuang; Wei, Xuemei
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 106
• Page End: 126
• Publication Date: 2019-06
• Subjects: Tumor growth -- Free boundary problem -- Angiogenesis -- Stationary solution -- The global solution -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.10.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we consider a free boundary problem modeling tumor growth with angiogenesis. The model is a free boundary problem of a system of partial differential equations. With Robin boundary, the model contains an ordinary differential equation describing the radius of tumor cell and two parabolic equations describing the evolution of nutrient concentration and inhibitor concentration, respectively. We study the number of the stationary solution of above problem, the existence and uniqueness of local solution and global solution, and the asymptotic behavior of the solution.