Un lien entre le coÛt des contrÔles rapides pour l'équation de la chaleur 1-D et l'uniforme contrÔlabilité d'une équation de transport-diffusion 1-D

Pierre Lissy

doi:10.1016/j.crma.2012.06.004

Un lien entre le coÛt des contrÔles rapides pour l'équation de la chaleur 1-D et l'uniforme contrÔlabilité d'une équation de transport-diffusion 1-D

Translated title of the contribution: A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation

Pierre Lissy

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

Abstract

In this Note, we explain how results on the cost of the null-controllability of the one-dimensional heat equation in small time can be used to bound from above the cost of the null-controllability of a one-dimensional transport-diffusion equation in the vanishing viscosity limit. We improve previous results about the minimal time needed to obtain the exponential decrease of the cost of the control and explain what would provide the usual conjecture concerning the cost of fast controls for the heat equation.

Translated title of the contribution	A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation
Original language	French
Pages (from-to)	591-595
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	350
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2012.06.004
Publication status	Published - 1 Jun 2012

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AB - In this Note, we explain how results on the cost of the null-controllability of the one-dimensional heat equation in small time can be used to bound from above the cost of the null-controllability of a one-dimensional transport-diffusion equation in the vanishing viscosity limit. We improve previous results about the minimal time needed to obtain the exponential decrease of the cost of the control and explain what would provide the usual conjecture concerning the cost of fast controls for the heat equation.

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ER -

Un lien entre le coÛt des contrÔles rapides pour l'équation de la chaleur 1-D et l'uniforme contrÔlabilité d'une équation de transport-diffusion 1-D

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