A model of morphogen transport in the presence of glypicans II

The model of morphogen transport introduced by Hufnagel et al. consisting of two evolutionary PDEs of reaction-diffusion type and three ODEs posed on a rectangular domain (−L,L)×(0,ϵH) is analysed. We prove that the problem is globally well-posed and that the corresponding solutions converge as ϵ tends to 0 to the unique solution of the one dimensional (i.e. posed on (−L,L)) system, which was analysed in previous paper. Main difficulties in the analysis stem from the presence of a singular source term - a Dirac Delta, combined with no smoothing effect in the ODE part of the system.