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

Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Timothy McCoy, Andrew J. Sommese

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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 μγ symmetry breaking bifurcation branches. Furthermore, we study the stability of both radially symmetric and radially asymmetric stationary solutions.

Original languageEnglish (US)
Pages (from-to)326-334
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume237
Issue number1
DOIs
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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