On the null-controllability of a radiative heat transfer system

Mohamed Ghattassi; Takéo Takahashi

doi:10.1016/j.ejcon.2021.03.003

On the null-controllability of a radiative heat transfer system

Mohamed Ghattassi, Takéo Takahashi

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.

Original language	English (US)
Pages (from-to)	143-151
Number of pages	9
Journal	European Journal of Control
Volume	59
DOIs	https://doi.org/10.1016/j.ejcon.2021.03.003
State	Published - Apr 23 2021
Externally published	Yes

ASJC Scopus subject areas

General Engineering

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10.1016/j.ejcon.2021.03.003

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title = "On the null-controllability of a radiative heat transfer system",

abstract = "This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.",

author = "Mohamed Ghattassi and Tak{\'e}o Takahashi",

note = "KAUST Repository Item: Exported on 2022-06-15 Acknowledgements: The authors would like to thank Bilel Hadri a computational scientist from the KAUST Supercomputing Lab for helping to run their 3D code on Shaheen, the enlightening discussions and the advice. For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. This material is based upon work supported by Tamkeen under the NYU Abu Dhabi Research Institute grant CG002 This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1016/j.ejcon.2021.03.003",

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N1 - KAUST Repository Item: Exported on 2022-06-15 Acknowledgements: The authors would like to thank Bilel Hadri a computational scientist from the KAUST Supercomputing Lab for helping to run their 3D code on Shaheen, the enlightening discussions and the advice. For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. This material is based upon work supported by Tamkeen under the NYU Abu Dhabi Research Institute grant CG002 This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2021/4/23

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N2 - This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.

AB - This paper studies the null controllability for radiative conductive convective heat transfer system in a grey, semi-transparent, scattering and bounded domain with control acting locally in a subset. The well-posedness of PDE is proved by the Banach fixed point theorem. Moreover, the null controllability proof is based on a fixed point argument and Carleman estimates in the presence of source terms, and it avoids tackling the linearized problems. Finally, a numerical experiment is included to validate the theoretical results.

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JO - European Journal of Control

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On the null-controllability of a radiative heat transfer system

Abstract

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