Volume 26, 2020
|Number of page(s)||34|
|Published online||17 December 2020|
Null controllability of the heat equation in pseudo-cylinders by an internal control
Sorbonne Université, Laboratoire Jacques-Louis Lions,
* Corresponding author: firstname.lastname@example.org
Accepted: 16 July 2020
In this paper we prove the null controllability of the heat equation in domains with a cylindrical part and limited by a Lipschitz graph. The proof consists mainly on getting a Carleman estimate which presents the usual absorption properties. The main difficulty we face is the loss of existence of the usual weighted function in C2 smooth domains. In order to deal with this, we use its cylindrical structure and approximate the system by the same system stated in regular domains. Finally, we show some applications like the controllability of the semi-linear heat equation in those domains.
Mathematics Subject Classification: 35D30 / 93B05 / 93C20
Key words: Carleman inequalities / heat equation / Lipschitz domains / null controllability
© EDP Sciences, SMAI 2020
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