Bifurcacions genériques d'atractors en sistemes de reacció i difusió
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	1981
Resum:	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.
Drets:	Tots els drets reservats.
Llengua:	Català
Document:	Article ; recerca ; Versió publicada
Publicat a:	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

90 p, 1.3 MB

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