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 (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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-di usion 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.

Domaines: Analyse numérique [cs.NA]

Pierre Lissy. 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.. C. R.Acad.Sci.Paris Ser. I, 2012. ⟨hal-00702497⟩