Stationary solutions of a free boundary problem modeling the growth of tumors with Gibbs–Thomson relation

In this paper we study a free boundary problem modeling tumor growth. The model consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumors, respectively, and a first-order partial differential equation governing the free boundary, on which a Gibbs–Thomson relation is taken into account. We first show that the problem may have none, one or two radial stationary solutions depending on model parameters. Then by bifurcation analysis we show that there exist infinite many branches of non-radial stationary solutions bifurcating from given radial stationary solution. The result implies that cell-to-cell adhesiveness is the key parameter which plays a crucial role on tumor invasion.