Optimal control problems of parabolic fractional sturm liouville equations in a star graph

2021/05/04 by G. Leugering, Leugering, G., G. Mophou +5 · 2 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.01720

openalex publication_date 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Numerical approximation of fractional diffusion equations on metric graphs
• Fractional Sturm-Liouville problem on metric graphs

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