Wenrui Hao
Afilliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame
Title: Computing steady-state solutions for a free boundary problem modeling tumor growth by stokes equation
Abstract: We consider a free boundary problem modeling tumor growth in
fluid-like tissue. The model equations include a diffusion equation
for the nutrient concentration, and the Stokes equation with a
source which represents the proliferation of tumor cells. For any
positive radius $R$ there exists a unique radialy symmetric
stationary solution. We setup a discetization of the system yielding
a polynomial system. A sequence $\mu/\gamma$ there exist
symmetry-breaking bifurcation branches of solutions has been
numerically verified by tracking the discetized system. Furthermore,
the nonlinear stability of both radialy symmetric stationary
solution and non-radialy symmetric stationary solution are
presented.
