SYMMETRY-BREAKING COMBINED LATITUDE-LONGITUDE BIFURCATIONS FOR A FREE BOUNDARY PROBLEM MODELING SMALL PLAQUES

. In [3] a mathematical model of the initiation and development of atherosclerosis involving LDL and HDL cholesterol, macrophages, and foam cells was introduced. The model is a highly nonlinear and coupled system of PDEs with a free boundary - the interface between the plaque and the blood flow. We establish infinite branches of symmetry-breaking stationary solutions that bifurcate from the stationary annular solution in the combined longitudelatitude direction. After establishing various estimates for our PDE system, the Crandall-Rabinowitz theorem is applied to prove our main bifurcation theorem.