Point condensations of a model for fungal development

We study the stationary solutions for a reaction-diffusion system of activa tor-inhibitor type which arises as a model for fungal development. Under th e condition that the activator diffuses slowly and the inhibitor diffuses v ery quickly we rigorously construct solutions which show single peak patter n near the boundary or in the interior in the activator component and have nearly constant values in the other. We also establish the linear stability and instability of such solutions. (C) Academie des Sciences/Elsevier, Par is.