Attractors for nonautonomous multivalued evolution systems generated by time-dependent subdifferentials. (23rd September 2002)

• Record Type: Journal Article
• Authors: Yamazaki, Noriaki
• Is Part Of: Abstract and applied analysis. Volume 7:Number 9(2002)
• Page Start: 453
• Page End: 473
• Publication Date: 2002-09-23
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337502204042
• Languages: English
• ISSNs: 1085-3375

Abstract

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.