Asymptotic analysis of a mathematical model of the atherosclerosis development

Abstract

A mathematical model, which takes into account new experimental results about diverse roles of macrophages in the atherosclerosis development, is proposed. Using technic of upper and lower solutions, the existence and uniqueness of its positive solution are justified. After the nondimensionalization, small parameters are found and the multiscale analysis of the corresponding perturbed problem is performed when those parameters tend to zero. In particular, the limit two-dimensional problem, which is a coupled system of reaction–diffusion equations and ordinary differential equations, is derived; the asymptotic approximation is constructed; the uniform pointwise estimate for the difference between the solution of the original problem and the solution of the limit problem as well as the respective [Formula: see text]-estimates for the fluxes are proved.