Noriaki Yamazaki, "Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-Dependent Subdifferentials", Abstract and Applied Analysis, vol. 7, Article ID 217405, 21 pages, 2002. https://doi.org/10.1155/S1085337502204042
Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-Dependent Subdifferentials
In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of our multivalued semiflows from the viewpoint of attractors. In fact, assuming that the time-dependent subdifferential converges asymptotically to a time-independent one (in a sense) as time goes to infinity, we construct global attractors for nonautonomous multivalued dynamical systems and its limiting autonomous multivalued dynamical system. Moreover, we discuss the relationship between them.
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