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Article Dans Une Revue Journal of Differential Equations Année : 2016

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

Résumé

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.
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Dates et versions

hal-01134917 , version 1 (24-03-2015)
hal-01134917 , version 2 (02-04-2015)

Identifiants

Citer

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