Null-controllability of the Kolmogorov equation in the whole phase spaceReportar como inadecuado




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1 FRDP - Fédération de recherche Denis Poisson 2 IUF - Institut Universitaire de France 3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 4 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Keywords : controllability spectral inequality Carleman estimates unbounded domain





Autor: Jérôme Le Rousseau - Iván Moyano -

Fuente: https://hal.archives-ouvertes.fr/



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