Mean field type control with congestion

TL;DR

This paper studies a class of PDE systems in mean field control with congestion, establishing the existence and uniqueness of weak solutions via dual optimal control problems.

Contribution

It introduces a framework for weak solutions in mean field control with congestion and proves their existence and uniqueness.

Findings

Existence of weak solutions is proven.

Uniqueness of solutions is established.

Solutions are characterized as optima of dual control problems.

Abstract

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.