Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation |
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Authors: | Wenrui Hao Jonathan D Hauenstein Bei Hu Timothy McCoy Andrew J Sommese |
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Institution: | 1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, United States;2. Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, TX 77843, United States |
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Abstract: | 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 μ/γ symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions. |
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Keywords: | Free boundary problems Stationary solution Stokes equation Bifurcation Homotopy continuation Tumor growth |
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