An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain

Abstract

A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.