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).

Zoom meeting: Link