Large-time optimal observation domain for linear parabolic systems
Given a well-posed linear evolution system settled on a domain \Omega of \mathbb{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.
Authors
- Idriss Mazari (ORCID: https://orcid.org/0000-0002-6779-6731)
- Yannick Privat (ORCID: https://orcid.org/0000-0002-2039-7223)
- Emmanuel Trélat (ORCID: https://orcid.org/0000-0002-0656-7003)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Centre de Recherche en Mathématiques de la Décision (FR)
- Institut Universitaire de France (FR)
- Université Paris Cité (FR)
- Institut Élie Cartan de Lorraine (FR)
- Sorbonne Université (FR)
- Sorbonne Paris Cité (FR)
- Numerical Method (China) (CN)
- Laboratoire Jacques-Louis Lions (FR)
- Université Paris Dauphine-PSL (FR)
- Université de Lorraine (FR)
Publication Details
- Journal
- Annales de l Institut Henri Poincaré C Analyse Non Linéaire
- Published
- 2025-01-23
- DOI
- https://doi.org/10.4171/aihpc/152
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche