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Insensitizing controls for the heat equation with respect to boundary variations

Ervedoza, Sylvain; Lissy, Pierre; Privat, Yannick (2020), Insensitizing controls for the heat equation with respect to boundary variations. https://basepub.dauphine.psl.eu/handle/123456789/22314

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Insensibilisation.pdf (388.5Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03083177
Date
2020
Series title
Cahier de recherche du CEREMADE
Pages
24
Metadata
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Author(s)
Ervedoza, Sylvain
Institut de Mathématiques de Bordeaux [IMB]
Lissy, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Privat, Yannick cc
Institut de Recherche Mathématique Avancée [IRMA]
Abstract (EN)
This article is dedicated to insensitization issues of a quadratic functional involving the solution of the linear heat equation with respect to domains variations. This work can be seen as a continuation of [P. Lissy, Y. Privat, and Y. Simpor\'e. Insensitizing control for linear and semi-linear heat equations with partially unknown domain. ESAIM Control Optim. Calc. Var., 25:Art. 50, 21, 2019], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider boundary variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate insensitization, (ii) approximate insensitization combined with an exact insensitization for a finite-dimensional subspace, and (iii) exact insensitization. We provide positive answers to questions (i) and (ii) and partial results to question (iii).
Subjects / Keywords
heat equation; exact/approximate control; domain variations; insensitization properties; Brouwer fixed-point theorem

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