Continuation along bifurcation branches for a tumor model with a necrotic core

Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Yuan Liu, Andrew J. Sommese, Yong Tao Zhang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 languageEnglish (US)
Pages (from-to)395-413
Number of pages19
JournalJournal of Scientific Computing
Volume53
Issue number2
DOIs
StatePublished - 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

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