Asymptotic stability for a free boundary tumor model with angiogenesis

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:270

Article

Huang, Yaodan^1,2  Zhang, Zhengce²  Hu, Bei³ 

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[3] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA

关键词: Free boundary problems;    Tumor growth;    Angiogenesis;    Stationary solution;    Nonlinear stability;   

DOI  :  10.1016/j.jde.2020.08.050

来源: Elsevier

【 摘 要 】

In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn. Syst. 39 (2019) 2473-2510] that for this model, there exists a threshold value mu* such that the unique radially symmetric stationary solution is linearly stable under non-radial perturbations for 0 < mu < mu* and linearly unstable for mu >mu*. In this paper we further study the nonlinear stability of the radially symmetric stationary solution, which introduces a significant mathematical difficulty: the center of the limiting sphere is not known in advance owing to the perturbation of mode 1 terms. We prove a new fixed point theorem to solve this problem, and finally obtain that the radially symmetric stationary solution is nonlinearly stable for 0 < mu < mu* when neglecting translations. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free