Abstract :
In this paper we study the existence of classical solutions to a new model of skeletal development
in the vertebrate limb. The model incorporates a general term describing adhesion interaction between
cells and fibronectin, an extracellular matrix molecule secreted by the cells, as well as two
secreted, diffusible regulators of fibronectin production, the positively-acting differentiation factor
(“activator”) TGF-β, and a negatively-acting factor (“inhibitor”). Together, these terms constitute
a pattern forming system of equations. We analyze the conditions guaranteeing that smooth solutions
exist globally in time. We prove that these conditions can be significantly relaxed if we add a
diffusion term to the equation describing the evolution of fibronectin.
2004 Elsevier Inc. All rights reserved
