no. G2
Article de recherche - Équations aux dérivées partielles, Théorie du contrôle
A general existence theorem for a multi-valued control problem
Emamizadeh, Behrouz1, 2 ; Liu, Yichen3  ; Zivari-Rezapour, Mohsen4
1Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
2Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
3Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
4Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 195-202

In this paper, we propose a general existence theorem for a multi-valued control problem. The proof of the theorem is based on a decomposition result of the weak ☆ closure of the set containing all the multi-valued controls and the bathtub principle. We also obtain the optimality condition for the optimal control.

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DOI : 10.5802/crmath.568
Classification : 49J20, 49K20, 35J20
Keywords: multi-valued control, existence, uniqueness, decomposition, optimality condition

Emamizadeh, Behrouz  1 , 2   ; Liu, Yichen  3   ; Zivari-Rezapour, Mohsen  4

1 Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
2 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
3 Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
4 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {A general existence theorem for a multi-valued control problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {195--202},
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Emamizadeh, Behrouz; Liu, Yichen; Zivari-Rezapour, Mohsen. A general existence theorem for a multi-valued control problem. Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 195-202. doi: 10.5802/crmath.568

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