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

32 Citations (Scopus)

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

Fingerprint

Free Boundary Problem
Stationary Solutions
Tumors
Tumor
Branch
Bifurcation
Radially Symmetric Solutions
Tumor Growth
Systems of Partial Differential Equations
Growth
Modeling
Symmetry Breaking
Neoplasms
Partial differential equations
Free boundary problem
Model

All Science Journal Classification (ASJC) codes

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

Cite this

Hao, Wenrui ; Hauenstein, Jonathan D. ; Hu, Bei ; Liu, Yuan ; Sommese, Andrew J. ; Zhang, Yong Tao. / Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. In: Nonlinear Analysis: Real World Applications. 2012 ; Vol. 13, No. 2. pp. 694-709.
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Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. / Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong Tao.

In: Nonlinear Analysis: Real World Applications, Vol. 13, No. 2, 01.04.2012, p. 694-709.

Research output: Contribution to journalArticle

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