Controlling the spread of invasive biological species

Date: Thu. November 24, 2022
Event: FAU DCN-AvH Seminar
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: FAU DCN-AvH Seminar “Controlling the spread of invasive biological species”

Speaker: Prof. Maria Teresa Chiri
Affiliation: Department of Mathematics and Statistics Queen’s University (Canada)

Abstract. We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. We first analyze the optimal control of 1-dimensional traveling wave profiles. Using Stokes’ formula, explicit solutions are obtained, which in some cases require measure-valued optimal controls. Then we introduce a family of optimization problems for a moving set and show how these can be derived from the original parabolic problems, by taking a sharp interface limit. In connection with moving sets, we show some results on controllability, existence of optimal strategies, and necessary conditions. This is a joint work with Prof. Alberto Bressan (Penn State University) and Dr. Najmeh Salehi (Saint Mary’s College).

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