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

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 * * and a sequence of γ m such that, for every γ m (m > m * * ), symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solutions. MSC: Primary 35B35; 35K35; secondary 35Q80