Time: March 26, 2025, 11:00
Room: RICAM, SP2 416-1

Titel: Optimal control of a Fokker-Planck/transport equation with BV-drift using renormalized solutions

Abstract: 

This talk focuses on the bilinear optimal control of a Fokker-Planck equation, possibly in the degenerate case of a transport equation. We consider a drift field with very low regularity (specifically, BV-regularity in space), which necessitates the use of renormalized solutions, a technique developed by Ronald DiPerna and Pierre-Louis Lions. This foundational theory has been significantly extended by Luigi Ambrosio to encompass cases with BV-regular drift fields. The theory of renormalized solutions is essential not only for establishing the uniqueness of solutions to the controlled PDE but also serves as a method for defining these solutions. Our findings indicate that this approach is particularly natural in the context of optimal control.

I am going to outline the PDE-constrained optimization problem we have considered and present our functional-analytic framework concerning the existence of optimal controls and the corresponding optimality criteria.