Abstract
Well-posedness and large time convergence to the unique steady state are shown for a model which describes the spreading of morphogens by a nonlinear transport mechanism (transcytosis) and couples a quasilinear parabolic partial differential equation with an ordinary differential equation. A simpler model which assumes linear transport is also investigated for comparison. The analysis of both models requires the construction of specific Liapunov functionals. The study is supplemented by numerical simulations of the sensitivity of the models to the variation of their parameters.
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