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

• Autores: Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Timothy McCoy, Andrew J. Sommese
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 237, Nº 1, 2013, págs. 326-334
• Idioma: inglés
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• Resumen

  • 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.