Abstract and Applied Analysis
Volume 7 (2002), Issue 9, Pages 453-473
doi:10.1155/S1085337502204042
Attractors for nonautonomous multivalued evolution systems generated by time-dependent subdifferentials
Department of Mathematical Science, Common Subject Division, Muroran Institute of Technology, 27-1 Mizumoto-chō, Muroran 050-8585, Japan
Received 15 March 2002
Copyright © 2002 Noriaki Yamazaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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.