## Abstract

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R and 0 < ρ < R, there exists a radially-symmetric stationary solution with tumor free boundary r = R and necrotic free boundary r = ρ. The system depends on a positive parameter μ, which describes tumor aggressiveness, and for a sequence of values μ2 < μ3 <. . . , there exist branches of symmetry-breaking stationary solutions, which bifurcate from these values. Upon discretizing this model, we obtain a family of polynomial systems parameterized by tumor aggressiveness factor μ. By continuously changing μ using a homotopy, we are able to compute nonradial symmetric solutions. We additionally discuss linear and nonlinear stability of such solutions.

Original language | English (US) |
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Pages (from-to) | 395-413 |

Number of pages | 19 |

Journal | Journal of Scientific Computing |

Volume | 53 |

Issue number | 2 |

DOIs | |

State | Published - Nov 1 2012 |

## All Science Journal Classification (ASJC) codes

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