  We analyze a one dimensional version of a model of morphogen transport, a
biological process governing cell differentiation. The model was proposed by
Hufnagel et al. to describe the forming of morphogen gradient in the wing
imaginal disc of the fruit fly. In mathematical terms the model is a system of
reaction-diffusion equations which consists of two parabolic PDE's and three
ODE's. The source of ligands is modelled by a Dirac Delta. Using semigroup
approach and $L_1$ techniques we prove that the system is well-posed and
possesses a unique steady state. All results are proved without imposing any
artificial restrictions on the range of parameters.
