Cell cycle control and bifurcation for a free boundary problem modeling tissue growth

Wenrui Hao, Bei Hu, Andrew J. Sommese

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider a free boundary problem for a system of partial differential equations, which arise in a model of cell cycle with a free boundary. For the quasi steady state system, it depends on a positive parameter β, which describes the signals from the microenvironment. Upon discretizing this model, we obtain a family of polynomial systems parameterized by β. We numerically find that there exists a radially-symmetric stationary solution with boundary r = R for any given positive number R by using numerical algebraic geometry method. By homotopy tracking with respect to the parameter β, there exist branches of symmetry-breaking stationary solutions. Moreover, we proposed a numerical algorithm based on Crandall-Rabinowitz theorem to numerically verify the bifurcation points. By continuously changing β using a homotopy, we are able to compute non-radially symmetric solutions. We additionally discuss control function β.

Original languageEnglish (US)
Pages (from-to)350-365
Number of pages16
JournalJournal of Scientific Computing
Issue number2
StatePublished - Aug 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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