A model of morphogen transport in the presence of glypicans I

We analyse 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 a 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 the semigroup approach and L1L1 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.