We study a nonlinear evolution equation associated with time-dependent subdifferential in a separable Hilbert space. In particular, we consider an asymptotically periodic system, which means that time-dependent terms converge to time-periodic terms as time approaches infinity. Then we consider the large-time behavior of solutions without uniqueness. In such a situation the corresponding dynamical systems are multivalued. In fact, we discuss the stability of multivalued semiflows from the view-point of attractors. Namely, the main object of this paper is to construct a global attractor for asymptotically periodic multivalued dynamical systems, and to discuss the relationship to one for the limiting periodic systems.
Submitted April 17, 2004. Published September 10, 2004.
Math Subject Classifications: 35B35, 35B40, 35B41, 35K55, 35K90.
Key Words: Subdifferentials; multivalued dynamical systems; attractors; stability.
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| Noriaki Yamazaki |
Department of Mathematical Science
Common Subject Division
Muroran Institute of Technology
27-1 Mizumoto-cho, Muroran, 050-8585, Japan
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