Felix-Klein-Kolloquium: Mean-Field Control for a Diffusion Aggregation System with Coulomb lnteraction

The mean-field control problem for a multi-dimensional diffusion-aggregation system with Coulomb interaction [the so called parabolic elliptic Keller-Segel system] is considered. The existence of optimal control is proved through the Gamma-convergence of the control problem of a regularized particle control problem. There are three building blocks in the whole argument.

Firstly, for the optimal control problem on the particle level, instead of using the classical method for a stochastic system, we study directly the control problem of a high-dimensional parabolic equation, i.e. the corresponding Liouville equation of the particle system.

Secondly, the strong propagation of chaos result for moderate interacting system is obtained by combining the convergence in probability and relative entropy method. Due to this strong mean field limit result, we avoid the compact support requirement for control functions, which has been often used in the literature.

Thirdly, because of strong the aggregation effect, additional difficulties arise from the control function in the well-posedness theory, so that the known method for the multi-dimensional Keller-Segel equation cannot be directly applied. lnstead, we use a combination of a local existence result and a bootstrap argument to obtain the global solution in the sub-critical regime.

Referentin: Prof. Dr. Li Chen, Universität Mannheim

Zeit: 17:15 - 18:30 Uhr

Ort: Gebäude 48, Raum 210

Die Vorträge des Felix-Klein-Kolloquiums finden jeweils um 17.15 Uhr im Raum 210 des Mathematik-Gebäudes 48 statt. Zuvor gibt es ab 16.45 Uhr die Gelegenheit, die Sprecherin oder den Sprecher beim Kolloquiumstee in Raum 580 zu treffen.