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arXiv · 2108.09321

On the Optimal Control of Propagation Fronts

Alberto Bressan·Maria Teresa Chiri·Najmeh Salehi
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Abstract

We consider a controlled reaction-diffusion equation, motivated by a pest eradication problem. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. In this direction, the first part of the paper studies 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. In the last section we introduce a family of optimization problems for a moving set. We show how these can be derived from the original parabolic problems, by taking a sharp interface limit.

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Alberto Bressan, Maria Teresa Chiri, Najmeh Salehi. 2021-08-20. On the Optimal Control of Propagation Fronts. https://arxiv.org/abs/2108.09321

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