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