Nonnegative weak solutions for a mathematical model of atherosclerosis in the early stage

We consider a mathematical model of the initiation and development of atherosclerosis in the early stage, defined in different domains. The existence of nonnegative weak solutions is proved via studying an auxiliary system with absolute value terms and applying a novel semi-discrete, operator splitting numerical scheme. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify our assumptions in model building and theoretical analysis. The framework we developed can also be used for nonlinear reaction–diffusion systems defined in other different domains with more complex coupling conditions.