Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
Ore: 11.00
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