Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:237

Article

Hao, Wenrui¹  Hauenstein, Jonathan D.²  Hu, Bei¹  McCoy, Timothy¹  Sommese, Andrew J.¹ 

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

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Free boundary problems;    Stationary solution;    Stokes equation;    Bifurcation;    Homotopy continuation;    Tumor growth;   

DOI  :  10.1016/j.cam.2012.06.001

来源: Elsevier

【 摘 要 】

We consider a free boundary problem modeling tumor growth where the model equations include a diffusion equation for the nutrient concentration and the Stokes equation for the proliferation of tumor cells. For any positive radius R, it is known that there exists a unique radially symmetric stationary solution. The proliferation rate mu and the cell-to-cell adhesiveness gamma are two parameters for characterizing aggressiveness of the tumor. We compute symmetry-breaking bifurcation branches of solutions by studying a polynomial discretization of the system. By tracking the discretized system, we numerically verified a sequence of mu/gamma symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free