Do global attractors depend on boundary conditions?
Bernold FiedlerInstitut fur Mathematik I Freie Universitat Berlin Arnimallee 2-6 D-14195 Berlin Germany
We consider global attractors of infinite dimensional dynamical systems given by dissipative partial differential equations on the unit interval 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 . 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.
Cite this article
Bernold Fiedler, Do global attractors depend on boundary conditions?. Doc. Math. 1 (1996), pp. 215–228DOI 10.4171/DM/11