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<p>We are concerned with a space-time fractional parabolic initial-boundary value problem of Sturm-Liouville type in a general star graph with mixed Dirichlet and Neumann boundary controls. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. Using the notion of no-regret control introduced by Lions, we prove the existence, uniqueness, and characterize the low regret control of a quadratic boundary optimal control problem, then we prove that this low regret control converges to the no-regret control and we provide the associated optimality systems and conditions that characterize that no-regret control.</p>

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No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月28日

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  • Gisèle Mophou,
  • Maryse Moutamal,
  • Mahamadi Warma

摘要

We are concerned with a space-time fractional parabolic initial-boundary value problem of Sturm-Liouville type in a general star graph with mixed Dirichlet and Neumann boundary controls. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. Using the notion of no-regret control introduced by Lions, we prove the existence, uniqueness, and characterize the low regret control of a quadratic boundary optimal control problem, then we prove that this low regret control converges to the no-regret control and we provide the associated optimality systems and conditions that characterize that no-regret control.