A diffusion-consumption problem for oxygen in a living tissue perfused by capillaries

Abstract.

We study a mathematical model describing the nonlinear diffusion of oxygen in a living tissue, in presence of consumption due to metabolism. The tissue is perfused by a system of parallel capillaries in which oxygen is carried by the blood both in the form of gas freely diffusing in plasma and bound to hemoglobin. We prove global existence of a unique smooth solution to the resulting parabolic-hyperbolic system.