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Seminario Matematico e Fisico di Milano
Alberto Bressan
The Pennsylvania State University
Optimal control of propagation fronts and moving sets

Martedì 06 Giugno 2023, ore 16:30
Sala Consiglio 7^ piano, Dipartimento di Matematica ed. 14, Politecnico di Milano
We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. A simpler model is then derived, describing the controlled evolution of a contaminated set. The first part of the talk will focus on the optimal control of 1-dimensional traveling wave profiles. Namely, we seek a control with minimum norm which produces a traveling profile with a given speed. In turn, this leads to a family of optimization problems for a moving set, related to the original reaction-diffusion equation via a sharp interface limit. In connection with moving sets, the second part of the talk will present some results on controllability, existence of optimal strategies, and optimality conditions. Some open questions will be discussed.