Skip to Main content Skip to Navigation
Journal articles

Null-controllability of the Kolmogorov equation in the whole phase space

Abstract : We prove the null controllability, in arbitrary positive time, of the Kolmogorov equation ∂t + v · ∇x − ∆v with (x, v) ∈ R d × R d , with a control region of the form ω = ωx × ωv, where both ωx and ωv are open subsets of R d that are sufficiently spread out throughout the whole space R d. The proof is based on, on the one hand, a spectral inequality in R d with an observation on ωx, and, on the other hand, a Carleman-based observability inequality for a family of parabolic operators, ∂t − iv · ξ − ∆v, coupled with a knowledge of the decay rate of the free solutions of the Kolmogorov equation.
Complete list of metadatas

Cited literature [22 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01134917
Contributor : Jérôme Le Rousseau <>
Submitted on : Thursday, April 2, 2015 - 9:40:28 PM
Last modification on : Thursday, March 5, 2020 - 6:30:21 PM
Document(s) archivé(s) le : Tuesday, April 18, 2017 - 9:46:01 AM

File

Kolmogorov.pdf
Files produced by the author(s)

Identifiers

Citation

Jérôme Le Rousseau, Iván Moyano. Null-controllability of the Kolmogorov equation in the whole phase space. Journal of Differential Equations, Elsevier, 2016, 260, pp.3193-3233. ⟨10.1016/j.jde.2015.09.062⟩. ⟨hal-01134917v2⟩

Share

Metrics

Record views

1217

Files downloads

674