Some analytical results about a simple reaction-diffusion system for morphogenesis.
The reaction-diffusion system considered involves only one nonlinear term and is a gradient system. In a bifurcation analysis for the equilibrium states, the global existence of infinitely many solution branches can be shown by the method of Ljusternik-Schnirelmann. Their stability is studied. Using a Ljapunov functional it can be shown that the solutions of the time-dependent system converge to the equilibrium states.
D002454:Cell Differentiation; D004058:Diffusion; D008433:Mathematics; D008954:Models, Biological; D008956:Models, Chemical; D009024:Morphogenesis; D013997:Time Factors