Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph
Günter R. Leugering, Gisèle Massengo Mophou, Maryse Moutamal, Mahamadi Warma, Laboratoire L.A.M.I.A., Département de Mathématiques et Informatique, Université des Antilles, Campus Fouillole, 97159 Pointe-à-Pitre, (FWI), Guadeloupe, Laboratoire MAINEGE, Université Ouaga 3S, 06 BP 10347 Ouagadougou 06, Burkina Faso · Mathematical Control and Related Fields · 2022
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.