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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Null-controllability for the weakly dissipative fractional heat equations

Résumé

A. We prove that the fractional heat equations posed on the whole Euclidean space ℝ and associated with the operators (−∆) ∕2 are exactly null-controllable from control supports which are sufficiently "exponentially thick", when 0 < ≤ 1. This is a first positive null-controllability result in this weak dissipation regime. When 0 < < 1, we also give a necessary condition of the same form. This notion of exponential thickness is stronger than the geometric notion of thickness known to be a necessary and sufficient condition to obtain positive null-controllability results in the strong dissipation regime > 1. Inspired by the construction of the Smith-Volterra-Cantor sets, we also provide examples of non-trivial exponentially thick control supports.
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Dates et versions

hal-03913881 , version 1 (27-12-2022)
hal-03913881 , version 2 (13-09-2023)
hal-03913881 , version 3 (23-04-2024)

Identifiants

  • HAL Id : hal-03913881 , version 1

Citer

Paul Alphonse, Armand Koenig. Null-controllability for the weakly dissipative fractional heat equations. 2022. ⟨hal-03913881v1⟩
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