Avviso di seminario, Università di Trento
"Regularization by noise for transport and kinetic equations"
Martedì 31 ottobre 2017
*Luogo:* Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula
Seminari "-1"
*Ore*: 11.00
- *Relatore: *Ennio Fedrizzi (Applied Mathematical Department, ENSTA
ParisTech)
*Abstract: *For some differential equations the addition of a carefully
chosen, random noise term can produce a regularising effect (e.g. solutions
are more regular, or restored uniqueness).
I will first mention a few easy examples (ODEs) to introduce some of these
regularising mechanisms, then detail two cases where we have regularisation
for a PDE: the linear transport equation and a kinetic equation with force
term. I will present some classical results for these two equations,
related to well-posedness and regularity of solutions, that in the
stochastic setting can be obtained under weaker hypothesis. These results
are based on a careful analysis of the stochastic characteristics and the
regularising properties of some associated parabolic/elliptic PDE.
If time allows, I will conclude by introducing a new strategy of proof
based on stochastic exponentials and an associated parabolic PDE, which
allows to obtain, under even weaker hypothesis, well-posedness for
stochastic PDEs in a class of solutions which are only regular in mean.
This will be illustrated by an application to the transport equation.
*Referente: *Stefano Bonaccorsi