A mathematical model of the atherosclerosis development in thin blood vessels and its asymptotic approximation

Abstract

Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic of upper and lower solutions, the existence and uniqueness of its positive solution are justified. After the nondimensionalisation, small parameters are found. Then asymptotic approximation for the solution is constructed and justified with the help of asymptotic methods for boundary-value problems in thin domains. The results argue for the possibility to replace the complex $3D$ (dimensional) mathematical model with the corresponding simpler $2D$ model with sufficient accuracy measured by these small parameters.

20 pages, 1 figure

References in corpus (2)

• Asymptotic Approximation for the Solution to a Semi-linear Parabolic Problem in a Thick Fractal Junction
• Asymptotic analysis of a boundary-value problem in a thin cascade domain with a local joint

Cited by in corpus (3)

• Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks
• Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions
• Asymptotic analysis of a contact Hele-Shaw problem in a thin domain