Calculus of Variations and Geometric Measure Theory
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A. Bressan - M. T. Chiri - N. Salehi

On the Optimal Control of Propagation Fronts

created by chiri on 20 Aug 2021

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Submitted Paper

Inserted: 20 aug 2021
Last Updated: 20 aug 2021

Year: 2021

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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