Abstract and Applied Analysis (Jan 2002)

Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-Dependent Subdifferentials

  • Noriaki Yamazaki

DOI
https://doi.org/10.1155/S1085337502204042
Journal volume & issue
Vol. 7, no. 9
pp. 453 – 473

Abstract

Read online

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.