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Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph

  • * Corresponding author: Mahamadi Warma

    * Corresponding author: Mahamadi Warma

The third author is supported by the Deutscher Akademischer Austausch Dienst/German Academic Exchange Service (DAAD). The fourth author is partially supported by the AFOSR under Award NO: FA9550-18-1-0242 and by the US Army Research Office (ARO) under Award NO: W911NF-20-1-0115

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  • 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.

    Mathematics Subject Classification: 35J20,49J45,49J20.


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  • Figure 1.  A sketch of a star graph with n edges

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