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

作者：Hao, Wenrui^*; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J.

来源：Journal of Computational and Applied Mathematics, 2013, 237(1): 326-334.

DOI：10.1016/j.cam.2012.06.001

• Free boundary problems
• Stationary solution
• Stokes equation
• Bifurcation
• Homotopy continuation
• Tumor growth

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.

• 出版日期2013-1-1