PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Svetlana Katok, Anatole Katok, Yakov Pesin.

Abstract:
Title:	On some asymptotic problems for stochastic partial differential equations ***THIS TALK WILL TAKE PLACE IN THE SYNERGISTIC ROOM ****
Seminar:	Center for Dynamics and Geometry Seminar
Speaker:	Sandra Cerrai, Universita di Firenze
In my talk I try to give an overview of a series of results which I have obtained in the last years and which concern some asymptotic problems for a class of PDEs (mainly of reaction-diffusion type) perturbed by a noisy term. I start from the analysis of their long-time behavior and I investigate the existence and uniqueness of invariant measures and their ergodic properties. I also try to explain what is the role played by the stochastic perturbation in the stabilization of solutions. Concerning the role played by the stochastic perturbation of PDEs, I will introduce some results on large deviations, both for the path and for the invariant measures of solutions, in the case of systems of reaction diffusion equations of Ginzburg-Landau type, perturbed by a noise of multiplicative type. I will conclude my talk describing some other limiting results for SPDEs, such as the Smoluchowski-Kramers approximation for the stochastic damped wave equation and the averaging principle.