Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core

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

Research output: Contribution to journalArticle

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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 numbers ρ<R, there exists a radially symmetric stationary solution with tumor boundary r = R and necrotic core boundary r=ρ. The system depends on a positive parameter μ, which describes the tumor aggressiveness. There also exists a sequence of values μ 2< μ3<⋯ for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric solution branch.

Original languageEnglish (US)
Pages (from-to)694-709
Number of pages16
JournalNonlinear Analysis: Real World Applications
Volume13
Issue number2
DOIs
StatePublished - Apr 1 2012

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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