Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840253 | Nonlinear Analysis: Theory, Methods & Applications | 2013 | 11 Pages |
Abstract
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.
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Authors
Marcin Małogrosz,