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ATTRACTORS FOR NONAUTONOMOUS MULTIVALUED EVOLUTION SYSTEMS GENERATED BY TIME-DEPENDENT

By Noriaki Yamazaki

Abstract

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 timeindependent 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. 1

Year: 2002
OAI identifier: oai:CiteSeerX.psu:10.1.1.187.5385
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