Volume 26, 2020
|Number of page(s)||43|
|Published online||14 February 2020|
Carleman estimates for time-discrete parabolic equations and applications to controllability*
Institut de Mathématiques de Toulouse & Institut Universitaire de France, UMR 5219, Université de Toulouse, CNRS, UPS IMT,
Toulouse Cedex 9, France.
2 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT, 31062 Toulouse Cedex 9, France.
** Corresponding author: email@example.com
Accepted: 22 November 2019
In this paper, we prove a Carleman estimate for a time-discrete parabolic operator under some condition relating the large Carleman parameter to the time step of the discretization scheme. This estimate is then used to obtain relaxed observability estimates that yield, by duality, some controllability results for linear and semi-linear time-discrete parabolic equations. We also discuss the application of this Carleman estimate to the controllability of time-discrete coupled parabolic systems.
Mathematics Subject Classification: 35K20 / 65M06 / 93B05 / 93B07 / 93C55
Key words: Carleman estimates / time-discrete heat equation / observability / null controllability
© EDP Sciences, SMAI 2020
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