Abstract:

The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis
will be demonstrated through the proof of the existence of random
attractors for asymptotically compact dissipative RDS.

Key words: Random dynamical systems, asymptotic compactness, dissipativity, Random attractor, Sobolev compact embedding