## Abstract

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 language | English (US) |
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Pages (from-to) | 350-365 |

Number of pages | 16 |

Journal | Journal of Scientific Computing |

Volume | 56 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2013 |

## All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Numerical Analysis
- Engineering(all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics