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

Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Timothy McCoy, Andrew J. Sommese

• 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 ì and the cell-to-cell adhesiveness ã 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 ì/ã symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions.