Theoretical model for the growth before sporulation of a fungal population on solid substrate

This paper deals with a non-linear system consisting of two ordinary differential equations describing differentiated fungal phases, a diffusion equation of the oxygen density. The equations are coupled due to the influence of the oxygen density in the biomass growth and the oxygen consumption by the biomass. Its solution is investigated using a perturbation technique. An asymptotic formula is given for phase-change times of biomass at any depth inside the reactor. Is determined the maximal thickness of substrate in order that tall present biomass be in the competent phase in the moment previous to the sporulation at the open surface.