DIFFERENTIAL EQUATION SEMINAR
Department of Mathematics
University of Rome Tor Vergata

Date: Tuesday,  22nd February 2022
Time: 16:00-17:00  (Time in Rome)
Where: Aula Dal Passo  (+ Streaming via Microsoft Teams, see link below)

Speaker: Cristian Mendico (University of Rome Tor Vergata)

Title:  Asymptotic behavior of solutions to Hamilton-Jacobi-Bellmann equations

Abstract:
The analysis of the ergodic behavior of solutions to Hamilton-Jacobi-Bellmann equations has a long history going back to the seminal paper by [Lions, P.-L., Papanicolaou, G. and Varadhan,S.R.S]. Since this work, the subject has grown very fast and when the Hamiltonian is of Tonelli type a large number of results have been proved. A full characterization of the ergodic behavior of solutions to Tonelli Hamilton-Jacobi equations can be found in the celebrated weak KAM theory and Aubry-Mather theory. However, few results are available if the Hamiltonian fails to be Tonelli, i.e., the Hamiltonian is neither strictly convex nor coercive with respect to the momentum variable. In particular, such results cover only some specific structure and so, the general problem is still open. In this talk, I will present some recent results obtained in collaboration with Piermarco Cannarsa and Pierre Cardaliaguet concerning the long time-average behavior of solutions to Hamilton-Jacobi-Bellman equations. We will look, first, to the case of control of acceleration and, then, to sub-Riemannian control systems. Finally, we conclude this talk showing how the previous analysis applies to mean field game systems.

Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006

MS Teams Link for the streaming:

https://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b1cd9%40thread.tacv2/1644948272731?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9%22%7d
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