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We consider a simple mathematical model of distribution of morphogens
(signaling molecules responsible for the differentiation of cells
and the creation of tissue patterns) proposed by Lander, Nie and Wan
in 2002. The model consists of a system of two equations: a PDE of
parabolic type modeling the distribution of free morphogens with a
dynamic boundary condition and an ODE describing the evolution of
bound receptors. Three biological processes are taken into account:
diffusion, degradation and reversible binding. We prove existence
and uniqueness of solutions and its asymptotic behavior.