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arXiv · 2303.13978

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

G. Mophou·M. Moutamal·M. Warma
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Abstract

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.

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G. Mophou, M. Moutamal, M. Warma. 2023-03-24. No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph. https://arxiv.org/abs/2303.13978

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