Bifurcacions genériques d'atractors en sistemes de reacció i difusió

In this work we write down in some detail the bifurcation theory of stationary states of reaction-diffusion equations. First, we prove, adapting notes of looss on the Navier-Stokes equations, that under some weak hypothesis a reaction-diffusion equation defines a differentiable dynamical systems in the Sobolev space H2 with some boundary conditions . Then it is proven that a rest point where the infinitessimal generator of the linear part of the system has a spectrum in the left hand plane is stable . We prove then that when , depending on a parameter, a simple eigenvalue crosses to the right hand plane, a bifurcation appears (generically). In the last chapter we propose a model for dune formation, which does not have the pretension of being faithful, but which illustrates how the theory given is usefu