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SCUOLA NORMALE SUPERIORE Preprints di Matematica -n. 5 Maggio 2005
 

Summary: SCUOLA NORMALE SUPERIORE
Pisa
Preprints di Matematica - n. 5 Maggio 2005
Stochastic Burgers-type equation
LUIGI MANCA
Stochastic Burgers-type equation
Luigi Manca
18 March 2005
Abstract
We consider stochastic semilinear partial differential equations with
burgers-type 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 Burgers-type equation perturbed by
noise in the Hilbert space H of all 2-periodic real functions

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics