61 research outputs found
Almost Periodic Passive Tracer Dispersion
The authors investigate the impact of external sources on the pattern
formation of concentration profiles of passive tracers in a two-dimensional
shear flow. By using the pullback attractor technique for the associated
nonautonomous dynamical system, it is shown that a unique time-almost periodic
concentration profile exists for time-almost periodic external source.Comment: latex fil
Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing
The full nonlinear dissipative quasigeostrophic model is shown to have a
unique temporally almost periodic solution when the wind forcing is temporally
almost periodic under suitable constraints on the spatial square-integral of
the wind forcing and the parameter, Ekman number, viscosity and the
domain size. The proof involves the pullback attractor for the associated
nonautonomous dynamical system
Lyapunov functions for cocycle attractors in nonautonomous difference equations
The construction of a Lyapunov function characterizing the pullback attraction of a cocycle attractor of a nonautonomous discrete time dynamical system involving Lipschitz continuous mappings is presented
On the Gap between Random Dynamical Systems and Continuous Skew Products
AMS 2000 subject classification: primary 37-02, 37B20, 37H05; secondary 34C27, 37A20.We review the recent notion of a nonautonomous dynamical system (NDS), which has been introduced as an abstraction of both random dynamical systems and continuous skew product flows. Our focus is on fundamental analogies and discrepancies brought about by these two classes
of NDS. We discuss base dynamics mainly through almost periodicity and almost automorphy, and we emphasize the importance of these concepts for NDS which are generated by differential and difference equations. Nonautonomous dynamics is presented by means of representative examples. We also mention several natural yet unresolved questions
Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay
We prove the existence of a stationary random solution to a delay random ordinary differential system which attracts all other solutions in both pullback and forwards senses. The equation contains a one-sided dissipative Lipschitz term without delay, while the random delay appears in a globally Lipschitz
one. The delay function only needs to be continuous in time. Moreover, we also prove that the split implicit Euler scheme associated to the random delay differential system generates a discrete time random dynamical system which also possesses a stochastic stationary solution with the same attracting property, and which converges to the stationary solution of the delay random
differential equation pathwise as the stepsize goes to zero
Attractors for 2D-Navier-Stokes models with delays
The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays,
etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation
Global and Pullback Attractors of Set-Valued Skew Product Flows
We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle mapping (coming from a nonautonomous differential equation or inclusion) driven by another, autonomous,system. Absorptivity conditions which ensure the existence of several types of
attractors for such set-valued systems are established. The topological properties of and relations between these attractors, in forward and pullback senses and their strong and weak versions are analyzed. Several illustrative examples are also provided
Weak Pullback Attractors of Non-Autonomous Difference Inclusions
Weak pullback attractors are defined for non-autonomous difference inclusions and their existence and upper semi continuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for (at least) a single trajectory rather than all trajectories at each starting point. The concept is thus useful, in particular, for discrete time control systems
- …