Avviso di seminario, Università di Trento
Parabolic theory of bi-Laplacians
giovedì 8 febbraio 2018
*Luogo: *Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula
Seminari "-1"
*Ore*: 11.00
Relatore:
- Delio Mugnolo (Università di Hagen - Germania)
Abstract:
The integral kernel of the semigroup generated by the bi-Laplacian on
$\mathbb R^d$ has been studied in several papers by E.B. Davies, while
other authors have successively studied positivity issues. Most of these
properties strongly depend on the fact that the bi-Laplacian acts on
functions in $H^4(\mathbb R)$ as the square of the Laplacian; this is not
true anymore if functions on bounded domains with generic boundary
conditions are considered. We are going to show how the properties of the
semigroup generated by bi-Laplacians on intervals and, more generally,
network-like spaces strongly depend on the boundary conditions. Our most
surprising finding is that, upon allowing the system enough time to reach
diffusive regime,
the parabolic equations driven by certain realizations of the bi-Laplacian
on networks display Markovian features: analogous results seem to be
unknown even in the classical case of domains.
This is joint work with Federica Gregorio.
*Referente: *Stefano Bonaccorsi