Optimal control problems of parabolic fractional sturm liouville equations in a star graph
Abstract
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.
Keywords
Cite
@article{arxiv.2105.01720,
title = {Optimal control problems of parabolic fractional sturm liouville equations in a star graph},
author = {G. Leugering and G. Mophou and M. Moutamal and M. Warma},
journal= {arXiv preprint arXiv:2105.01720},
year = {2022}
}