Bifurcacions genériques d'atractors en sistemes de reacció i difusió
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Date: |
1981 |
Abstract: |
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. |
Rights: |
Tots els drets reservats. |
Language: |
Català |
Document: |
Article ; recerca ; Versió publicada |
Published in: |
Publicacions de la Secció de Matemàtiques, V. 24 (1981) p. 73-162, ISSN 0210-2978 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsSeccioMatematiques/article/view/37436
DOI: 10.5565/PUBLMAT_24181_02
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Record created 2009-11-12, last modified 2022-09-10