**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.