Equilibrium model of a vascularized spherical carcinoma with central necrosis--some properties of the solution

Properties of the solutions of a nonlinear time-independent diffusion equation are studied. The equation arises in a model of a spherically symmetric vascularized carcinoma with a central necrotic core. The boundary value problem as posed possesses a constant solution when the nutrient consumption rate and deposition rate (from the vascular network) are equal. This solution can lose uniqueness at a critical tumor dimension which corresponds to the onset of instability with respect to deviations from that uniform equilibrium state.