Global asymptotic behavior of solutions for a parabolic-parabolic-ODE chemotaxis system modeling multiple sclerosis (Q2189787)

A model of multiple sclerosis consists of a chemotactic equation with logistic reaction term describing evolutions of the density of macrophages, a diffusion equation for concentration of a cytokine and an ordinary differential equation for the density of oligodendrocytes. The authors study existence, boundedness and asymptotic behavior of solutions of an initial-boundary value problem, and show their convergence to homogeneous steady states under some supplementary assumptions.