In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.

In this paper we consider a stochastic thin-film equation with a one dimensional Gaussian Stratonovych noise. We establish the existence of non-negative global weak martingale solution, and study its long time asymptotic properties. In particular, we show the solution almost surely converges to the average value of the initial condition. Furthermore, using the regularized equations and adapted entropy functionals, we establish the exponential asymptotic decay of the solution in the uniform norm.