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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2012

01.11.2012

Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core

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

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2012

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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 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 μ 2<μ 3<…, 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.
Vorheriger Artikel A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model
Nächster Artikel Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations

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Metadaten
Titel
Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core
verfasst von
Wenrui Hao
Jonathan D. Hauenstein
Bei Hu
Yuan Liu
Andrew J. Sommese
Yong-Tao Zhang
Publikationsdatum
01.11.2012
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2012
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-012-9575-x

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