| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 40 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2023029 | |
| Published online | 09 June 2023 | |
Optimal control problems of nonlocal interaction equations
1
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila,
Via Vetoio 1,
67100 Coppito, L’Aquila,
Italy
2
Institute of Mathematics, EPFL,
1015 Lausanne,
Switzerland
* Corresponding author: simone.fagioli@univaq.it
Received:
18
May
2022
Accepted:
14
April
2023
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of individuals is described by a suitable nonlocal transport equation, while the role of the population of agents is designed by the optimal control problem. This model has been first studied in [12] for a class of continuous nonlocal potentials, while in the present project we consider the case of mildly singular potentials in a gradient flow formulation of the target transport equation.
Mathematics Subject Classification: 49J20 / 45K05 / 492D25 / 92D25
Key words: Nonlocal transport equations / optimal control problems / Wasserstein distance / JKO scheme
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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