Strong Pullback Attractors of the Nonautonomous Suspension Bridge Equation with Variable Delay

In this paper, we consider the suspension bridge equation with variable delay. The long-time dynamics of the solutions for the suspension equations without delay effects have been investigated by many authors. But there are few works on suspension equations with delay. Moreover there are not many studies on attractors for other systems with delay. Thus, we study the existence of pullback attractor for the suspension equation with variable delay by using the theory of attractors for multivalued dynamical systems.

GENERALIZED SEMIFLOWS AND CHAOS IN MULTIVALUED DYNAMICAL SYSTEMS

This contribution addresses a possible description of the chaotic behavior in multivalued dynamical systems. For the multivalued system formulated via differential inclusion the practical conditions on the right-hand side are derived to guarantee existence of a solution, which leads to the chaotic behavior. Our approach uses the notion of the generalized semiflow but it does not require construction of a selector on the set of solutions. Several applications are provided by concrete examples of multivalued dynamical systems including the one having a clear physical motivation.

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

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.