Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Zhuang, Yuehong¹  Cui, Shangbin¹ 

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

关键词: Free boundary problem;    Tumor growth;    Well-posedness;    Stationary solution;    Asymptotic stability;   

DOI  :  10.1016/j.jde.2018.03.005

来源: Elsevier

【 摘 要 】

In this paper we study a free boundary problem modeling the growth of vascularized tumors. The model is a modification to the Byrne-Chaplain tumor model that has been intensively studied during the past two decades. The modification is made by replacing the Dirichlet boundary value condition with the Robin condition, which causes some new difficulties in making rigorous analysis of the model, particularly on existence and uniqueness of a radial stationary solution. In this paper we successfully solve this problem. We prove that this free boundary problem has a unique radial stationary solution which is asymptotically stable for large surface tension coefficient, whereas unstable for small surface tension coefficient. Tools used in this analysis are the geometric theory of abstract parabolic differential equations in Banach spaces and spectral analysis of the linearized operator. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free