Article Dans Une Revue Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis) Année : 2026

Large-time optimal observation domain for linear parabolic systems

Résumé

Given a well-posed linear evolution system settled on a domain $\Omega$ of $\R^d$, an observation subset $\omega\subset\Omega$ and a time horizon $T$, the observability constant is defined as the largest possible nonnegative constant such that the observability inequality holds for the pair $(\omega,T)$. In this article we investigate the large-time behavior of the observation domain that maximizes the observability constant over all possible measurable subsets of a given Lebesgue measure. We prove that it converges exponentially, as the time horizon goes to infinity, to a limit set that we characterize. The mathematical technique is new and relies on a quantitative version of the bathtub principle.

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Dates et versions

hal-04440343 , version 1 (05-02-2024)
hal-04440343 , version 2 (07-01-2026)

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Idriss Mazari, Yannick Privat, Emmanuel Trélat. Large-time optimal observation domain for linear parabolic systems. Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis), 2026, 43 (2), pp.345--370. ⟨10.4171/AIHPC/152⟩. ⟨hal-04440343v2⟩
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