Insensitizing controls for the heat equation with respect to boundary variations
PRIVAT, Yannick
TOkamaks and NUmerical Simulations [TONUS]
Institut de Recherche Mathématique Avancée [IRMA]
Institut universitaire de France [IUF]
TOkamaks and NUmerical Simulations [TONUS]
Institut de Recherche Mathématique Avancée [IRMA]
Institut universitaire de France [IUF]
PRIVAT, Yannick
TOkamaks and NUmerical Simulations [TONUS]
Institut de Recherche Mathématique Avancée [IRMA]
Institut universitaire de France [IUF]
< Reduce
TOkamaks and NUmerical Simulations [TONUS]
Institut de Recherche Mathématique Avancée [IRMA]
Institut universitaire de France [IUF]
Language
en
Article de revue
This item was published in
Journal de l'École polytechnique — Mathématiques. 2022, vol. Tome 9, p. 1397--1429
École polytechnique
English Abstract
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. ...Read more >
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).Read less <
English Keywords
heat equation
exact/approximate control
domain variations
insensitization properties
Brouwer fixed-point theorem
Origin
Hal imported