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

Abstract

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.

Keywords

• Free-boundary problem
• Stationary solution
• Bifurcation
• Symmetry-breaking
• Tumor growth