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We analyze a one dimensional version of a model of morphogen transport, abiological process governing cell differentiation. The model was proposed byHufnagel et al. to describe the forming of morphogen gradient in the wingimaginal disc of the fruit fly. In mathematical terms the model is a system ofreaction-diffusion equations which consists of two parabolic PDE's and threeODE's. The source of ligands is modelled by a Dirac Delta. Using semigroupapproach and $L_1$ techniques we prove that the system is well-posed andpossesses a unique steady state. All results are proved without imposing anyartificial restrictions on the range of parameters.

A model of morphogen transport in the presence of glypicans I