Transportation networks have been widely produced by nature.Neural networks,leaf vena-tures,vascular system,roots are example which share the property that the network transports auid or a current.In some cases,the formation of the network,during development of the individual,is based on a prematrix which can be seen has a porous media.The pressure produced by a source acts on this prematrix and generates new vessels.Physicists have proposed PDE models for to describe this interaction under the form of a singular system of parabolic/elliptic type.