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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2024

Bilinear optimal control of a one‐dimensional degenerate parabolic equation with a nonlocal term

Contrôle optimal bilinéaire pour une équation parabolique dégénérée 1D non-locale

Résumé

In this paper, a one‐dimensional degenerate parabolic equation involving a multiplicative control with a nonlocal space term represented by an integral kernel is considered. After some well‐posedness results, we derive several properties of the control‐to‐state mapping. We establish the existence of at least one optimal control and derive the first and the second conditions for optimality, giving the local uniqueness of an optimal control. Finally, we prove that we may expect the global uniqueness of the optimal control under additional assumptions.
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Dates et versions

hal-04561311 , version 1 (26-04-2024)

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Cyrille Kenne, Landry Djomegne, James Larrouy. Bilinear optimal control of a one‐dimensional degenerate parabolic equation with a nonlocal term. Mathematical Methods in the Applied Sciences, 2024, ⟨10.1002/mma.10148⟩. ⟨hal-04561311⟩
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