Stationary structures in a three dimensional reaction-diffusion system

We study stationary structures with radial symmetry in a three dimensional reaction-diffusion system inside a sphere, with partial and total reflection and absorption at the surface. The model corresponds to a piecewise linearized mimic of the Schlögl model for bistable reaction kinetics and could be thought of as a three dimensional version of the ballast resistor system. We show that the existence of stationary solutions can depend on the system size and carry out a linear stability analysis which indicates that the system presents zones of bistability in the space of relevant parameters.