TY - JOUR
T1 - On the optimal control of propagation fronts
AU - Bressan, Alberto
AU - Chiri, Maria Teresa
AU - Salehi, Najmeh
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/6/15
Y1 - 2022/6/15
N2 - 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.
AB - 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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U2 - 10.1142/S0218202522500257
DO - 10.1142/S0218202522500257
M3 - Article
AN - SCOPUS:85131883378
SN - 0218-2025
VL - 32
SP - 1109
EP - 1140
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 6
ER -