On the cost of null-control of an artificial advection-diffusion problem
Teacher at Lycée du parc des Loges, 1, boulevard des Champs-Élysées, 91012
2 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris Cédex 05, France
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