An inverse problem for equations of cerebral oxygen transport

Abstract A continuum steady-state model of cerebral oxygen transport is considered. It consists of two semilinear elliptic equations describing the distributions of blood and tissue oxygen concentrations. The inverse problem is to find unknown intensities of the sources of the equation for the blood oxygen transport. As conditions of overdetermination, the average values of the blood oxygen concentration in some neighborhoods of the sources, are taken. In addition, the reconstruction of the blood and tissue oxygen concentrations are also required. The existence theorem is proved without assumptions of smallness. The conditions for the uniqueness of the solution are established. A numerical algorithm based on the Tikhonov regularization method is constructed and its convergence is shown by a numerical example.