TY - JOUR

T1 - Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation

AU - Hao, Wenrui

AU - Hauenstein, Jonathan D.

AU - Hu, Bei

AU - McCoy, Timothy

AU - Sommese, Andrew J.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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 μ and the cell-to-cell adhesiveness γ 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 μγ symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions.

AB - 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 μ and the cell-to-cell adhesiveness γ 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 μγ symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions.

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U2 - 10.1016/j.cam.2012.06.001

DO - 10.1016/j.cam.2012.06.001

M3 - Article

AN - SCOPUS:84866125484

VL - 237

SP - 326

EP - 334

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1

ER -