SYMMETRY-BREAKING LONGITUDE BIFURCATION FOR A FREE BOUNDARY PROBLEM MODELING THE GROWTH OF TUMOR CORD IN THREE DIMENSIONS

In this paper, we analyze the free boundary problem in three dimensions describing the growth of tumor cords. The model consists of a reaction-diffusion equation describing the concentration sigma of nutrients and an elliptic equation describing the distribution of the internal pressure p. The model is defined in a bounded domain in R-3 whose boundary consists of two disjoint closed curves, the known interior part and the unknown exterior part. The concentration of nutrients outside the tumor region is denoted by sigma . We shall show that there is a positive integer n** and a sequence sigma over bar n such that for each sigma over bar n(n > n**), symmetry-breaking stationary solutions bifurcate from the annular stationary solution in the longitude direction.