 
Summary: SCUOLA NORMALE SUPERIORE
Pisa
Preprints di Matematica  n. 5 Maggio 2005
Stochastic Burgerstype equation
LUIGI MANCA
Stochastic Burgerstype equation
Luigi Manca
18 March 2005
Abstract
We consider stochastic semilinear partial differential equations with
burgerstype nonlinear terms. We prove existence and uniqueness of
an invariant measure and the existence of a solution for the correspon
dent Kolmogorov equation in a space based on the invariant measure.
We also prove the closability of the derivative operator and an inte
gration by parts formula. Finally, under smallness conditions on the
nonlinear term, we prove a PoincarŽe inequality, a logarithmic Sobolev
inequality and the ipercontractivity of the transition semigroup.
1 Introduction and setting of the problem
We are concerned with the following Burgerstype equation perturbed by
noise in the Hilbert space H of all 2periodic real functions
