Bifurcation analysis for a free-boundary tumor model with angiogenesis and inhibitor

• Main Authors: Zejia Wang, Huijuan Song, Suzhen Xu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-06-01
• Series: Boundary Value Problems
• Subjects: Free-boundary problem; Stationary solution; Bifurcation; Symmetry-breaking; Tumor growth
• Online Access: http://link.springer.com/article/10.1186/s13661-018-1014-y

Abstract This paper is concerned with the bifurcation phenomenon of a free-boundary problem modeling the tumor growth under the action of angiogenesis and inhibitor. Taking the surface tension coefficient γ as a bifurcation parameter, we prove that there exist a positive integer m∗∗ $m^{**}$ and a sequence of γm $\gamma_{m}$ such that, for every γm $\gamma_{m}$ ( m>m∗∗ $m>m^{**}$), symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solutions.