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Seminar on Analysis, Geometry, and PDEs


Tid: 2021-10-26 15:15 till 16:15
Plats: The talk is given on Zoom. If you wish to receive a link, please contact the organizer.
Kontakt: eskil [dot] rydhe [at] math [dot] lu [dot] se
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Stochastic epidemiological models and optimal control for the Fokker-Planck equation

Speaker: Jacob Körner, Würzburg

Abstract: We study an ensemble optimal control problem, where the state variable is subject to the Fokker-Planck equation (FP). This PDE is motivated by stochastic differential equations, which in turn arise from ODEs with parameters and initial conditions under uncertainty.

In this talk, we present standard epidemiological compartment models and derive its corresponding system of stochastic differential equations. The probability density functions of solutions to these stochastic equations are given by the corresponding (FP) equation with flux-zero boundary conditions. We show existence of sufficiently integrable weak solutions to (FP) and prove Fréchet differentiability and compactness of the control-to-state operator.

Finally, we formulate an expected-type cost functional and show existence and local uniqueness of optimal controls.

This is joint work with Alfio Borzì.