Null-controllability of the Kolmogorov equation in the whole phase spaceReport as inadecuate




Null-controllability of the Kolmogorov equation in the whole phase space - Download this document for free, or read online. Document in PDF available to download.

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





Author: Jérôme Le Rousseau - Iván Moyano -

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



DOWNLOAD PDF




Related documents