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
SN - 0377-0427
VL - 237
SP - 326
EP - 334
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -