## STEFANO ROSSI

PhD Graduate**PhD program:**: XXXV

**supervisor**: G. Panati

**Thesis title:**Asymptotic and validity problems for Vlasov-type equations

In this thesis we study some asymptotic and validity problems concerning Vlasov-type
equations. In the first part of the work we focus on the Landau damping and the long-time
behavior of solutions of the Vlasov-HMF and Vlasov-Poisson equations. We do it by looking
at the scattering problem, where the asymptotic datum is fixed, in the style of the work [ 17,
Bibliog. Part I]. In the second part of the thesis we focus on validity problems for kinetic
equations with topological interaction. This interaction does not depend on the metric
distance but rather on the proximity rank among the agents and, in the last decade, has
been widely used to describe biological systems that exhibit collective behaviors.

**Research products**

11573/1584421 - 2022 -

**Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation**Benedetto, Dario; Caglioti, Emanuele; Rossi, Stefano - 01a Articolo in rivista

**paper:**ASYMPTOTIC ANALYSIS (Amsterdam: North-Holland) pp. 215-238 - issn: 0921-7134 - wos: WOS:000837159200003 (1) - scopus: 2-s2.0-85135747826 (1)

11573/1633437 - 2021 -

**MEAN-FIELD LIMIT FOR PARTICLE SYSTEMS WITH TOPOLOGICAL INTERACTIONS**Benedetto, D.; Caglioti, E.; Rossi, S. - 01a Articolo in rivista

**paper:**MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS (Berkeley, CA : Mathematical Sciences Publishers, 2013- Università Dell’Aquila, Italy: International Research Center for the Mathematics and Mechanics of Complex Systems) pp. 423-440 - issn: 2326-7186 - wos: WOS:000819472900005 (3) - scopus: 2-s2.0-85129262713 (2)