ERVEDOZA, Sylvain; LISSY, Pierre; PRIVAT, Yannick

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ERVEDOZA, Sylvain
Institut de Mathématiques de Bordeaux [IMB]

LISSY, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

PRIVAT, Yannick
TOkamaks and NUmerical Simulations [TONUS]
Institut de Recherche Mathématique Avancée [IRMA]
Institut universitaire de France [IUF]

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Journal de l'École polytechnique — Mathématiques. 2022, vol. Tome 9, p. 1397--1429

École polytechnique

Résumé en anglais

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).< Réduire

Mots clés en anglais

heat equation

exact/approximate control

domain variations

insensitization properties

Brouwer fixed-point theorem

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Insensitizing controls for the heat equation with respect to boundary variations

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