Asymptotic behavior of solutions of a free-boundary tumor model with angiogenesis. (December 2018)

• Record Type: Journal Article
• Authors: Zhuang, Yuehong
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 86
• Page End: 105
• Publication Date: 2018-12
• Subjects: Tumor spheroid -- Angiogenesis -- Free boundary problem -- Well-posedness -- Asymptotic stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.05.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with a free boundary problem modeling the growth of solid tumor spheroid with angiogenesis. The model comprises a coupled system of two elliptic equations describing the distribution of nutrient concentration σ and inner pressure p within the tumor tissue. Angiogenesis results in a new boundary condition ∂ n σ + β σ − σ ¯ = 0 instead of the widely studied condition σ = σ ¯ over the moving boundary, where β is a positive constant. We first prove that this problem admits a unique radial stationary solution, and this solution is globally asymptotically stable under radial perturbations. Then we establish local well-posedness of the problem and study asymptotic stability of the radial stationary solution under non-radial perturbations. A positive threshold value γ ∗ is obtained such that the radial stationary solution is asymptotically stable for γ > γ ∗ and unstable for 0 < γ < γ ∗ .