Geodesic
Do global attractors depend on boundary conditions?
Documenta mathematica, Tome 1 (1996), pp. 215-228.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider global attractors of infinite dimensional dynamical systems given by dissipative partial differential equations $$u_t=u_{xx}+f(x,u,u_x) $$ on the unit interval $ 0 x 1 $ under separated, linear, dissipative boundary conditions. Global attractors are called orbit equivalent, if there exists a homeomorphism between them which maps orbits to orbits. The global attractor class is the set of all equivalence classes of global attractors arising for dissipative nonlinearities $f$. We show that the global attractor class does not depend on the choice of boundary conditions. In particular, Dirichlet and Neumann boundary conditions yield the same global attractor class. 
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     author = {Fiedler, Bernold},
     title = {Do global attractors depend on boundary conditions?},
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     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1996__1__a9/}
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Fiedler, Bernold. Do global attractors depend on boundary conditions?. Documenta mathematica, Tome 1 (1996), pp. 215-228. http://geodesic.mathdoc.fr/item/DOCMA_1996__1__a9/