Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis

Abstract

We study an atherosclerosis model described by a reaction-diffusion system of three equations, in one dimension, with homogeneous Neumann boundary conditions. The method of upper and lower solutions and its associ-ated monotone iteration (the monotone iterative method) are used to establish existence, uniqueness and boundedness of global solutions for the problem. Up-per and lower solutions are derived for the corresponding steady-state problem. Moreover, solutions of Cauchy problems defined for time-dependent system are presented as alternatives upper and lower solutions. The stability of constant steady-state solutions and the asymptotic behavior of the time-dependent so-lutions are studied.