Null controllability of Kolmogorov-type equations

Null controllability of Kolmogorov-type equations

We study the null controllability of Kolmogorov-type equations ∂t f + v ∂x f − ∂2 v f = u(t, x, v)1ω(x, v) in a rectangle , under an additive control supported in an open subset ω of . For γ = 1, with periodic-type boundary conditions, we prove that null controllability holds in any positive time, with any control support ω. This improves the previous result by Beauchard and Zuazua (Ann Ins H P...

Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type

The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator ∂ x + |x|∂ y (γ > 0) in the rectangle (x, y) ∈ (−1, 1)×(0, 1) or with the Kolmogorov-type operator v∂xf+∂ vf (γ ∈ {1, 2}) in the rectangle (x, v) ∈ T×(−1, 1), under an additive control supported in an open subset ω ...

On the null-controllability of diffusion equations

Null–controllability of One–dimensional Parabolic Equations

We prove the interior null–controllability of one–dimensional parabolic equations with time independent measurable coefficients.

Null Controllability Results for Degenerate Parabolic Equations

The null controllability of parabolic operators in bounded domains, with both boundary or locally distributed controls, is a well-established property, see, e.g., (Bensoussan et al., 1993) and (Fattorini, 1998). Such a property brakes down, however, for degenerate parabolic operators even when degeneracy occurs on ”small” subsets of the space domain, such as subsets of the boundary. This talk w...