| Issue |
ESAIM: COCV
Volume 19, Number 4, October-December 2013
|
|
|---|---|---|
| Page(s) | 1209 - 1224 | |
| DOI | https://doi.org/10.1051/cocv/2013048 | |
| Published online | 27 August 2013 | |
On the cost of null-control of an artificial advection-diffusion problem
1
Teacher at Lycée du parc des Loges, 1, boulevard des Champs-Élysées, 91012
Évry,
France
pierre.cornilleau@ens-lyon.org
2
Laboratoire Jacques-Louis Lions, Université Pierre et Marie
Curie, 75252
Paris Cédex 05,
France
guerrero@ann.jussieu.fr
Received:
22
June
2012
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
Mathematics Subject Classification: 35K57 / 93B05
Key words: Vanishing viscosity / controllability / heat equation / Carleman
© EDP Sciences, SMAI, 2013
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