Bifurcacions genériques d'atractors en sistemes de reacció i difusió

• Calsina i, Àngel ^[1]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Nº 24, 1981, págs. 73-162
• Idioma: catalán
• DOI: 10.5565/publmat_24181_02
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• Resumen

  • 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 useful.