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February  2009, 25(1): 343-361. doi: 10.3934/dcds.2009.25.343

Mathematical analysis of a model of morphogenesis

José Ignacio Tello 1,

1. 

Departamento de Matemática Aplicada, E.U. Informática. Universidad Politécnica de Madrid, Ctra. de Valencia, Km. 7. 28031 - Madrid, Spain

Received  December 2006 Revised  November 2007 Published  June 2009

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.
Keywords: reaction diffusion equations, Morphogens, stability of solutions..
Mathematics Subject Classification: 92D15, 92B05, 35K35, 35K5.
Citation: José Ignacio Tello. Mathematical analysis of a model of morphogenesis. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 343-361. doi: 10.3934/dcds.2009.25.343
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