On the optimal control of propagation fronts

Author:

Bressan Alberto1,Chiri Maria Teresa1,Salehi Najmeh1

Affiliation:

1. Department of Mathematics, Penn State University, University Park, PA. 16802, USA

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.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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