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 longitude-latitude direction. After establishing various estimates for our PDE system, the Crandall-Rabinowitz theorem is applied to prove our main bifurcation theorem. [ABSTRACT FROM AUTHOR]