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Article Dans Une Revue Mathematical Control and Related Fields Année : 2022

Optimal Control Problems Of Parabolic Fractional Sturm-Liouville Equations In A Star Graph

Résumé

In the present paper we deal with parabolic fractional initial-boundary value problems of Sturm-Liouville type in an interval and in a general star graph. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. We prove the existence and uniqueness of solutions to a quadratic boundary optimal control problem and provide a characterization of the optimal contol via the Euler-Lagrange first order optimality conditions. We then investigate the analogous problems for a fractional Sturm-Liouville problem in a general star graph with mixed Dirichlet and Neumann boundary controls. The existence and uniqueness of minimizers, and the characterization of the first order optimality conditions are obtained in a general star graph by using the method of Lagrange multipliers.
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hal-03592801 , version 1 (01-03-2022)

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  • HAL Id : hal-03592801 , version 1

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Günter Leugering, Gisèle Mophou, Maryse Moutamal, Mahamadi Warma. Optimal Control Problems Of Parabolic Fractional Sturm-Liouville Equations In A Star Graph. Mathematical Control and Related Fields, In press. ⟨hal-03592801⟩
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