Null controllability of Grushin-type operators in dimension two.

K Beauchard, P Cannarsa, R Guglielmi - Journal of the European …, 2014 - ems.press
We study the null controllability of the parabolic equation associated with the Grushintype
operator A=∂ 2 x+| x| 2γ∂ 2 y (γ> 0) in the rectangle=(− 1, 1)×(0, 1), under an additive …

Null controllability of the heat equation using flatness

P Martin, L Rosier, P Rouchon - Automatica, 2014 - Elsevier
We derive in a direct and rather straightforward way the null controllability of the N-
dimensional heat equation in a bounded cylinder with boundary control at one end of the …

Null controllability of one-dimensional parabolic equations by the flatness approach

P Martin, L Rosier, P Rouchon - SIAM Journal on Control and Optimization, 2016 - SIAM
We consider linear one-dimensional parabolic equations with space dependent coefficients
that are only measurable and that may be degenerate or singular. Considering generalized …

[LIBRO][B] Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations

G Fragnelli, D Mugnai - 2016 - ams.org
We consider a parabolic problem with degeneracy in the interior of the spatial domain, and
we focus on observability results through Carleman estimates for the associated adjoint …

[HTML][HTML] 2D Grushin-type equations: minimal time and null controllable data

K Beauchard, L Miller, M Morancey - Journal of Differential Equations, 2015 - Elsevier
We study internal null controllability for degenerate parabolic equations of Grushin-type G
γ=∂ xx 2+| x| 2 γ∂ yy 2 (γ> 0), in the rectangle (x, y)∈ Ω=(− 1, 1)×(0, 1). Previous works …

Stackelberg–Nash null controllability for some linear and semilinear degenerate parabolic equations

FD Araruna, BSV Araújo, E Fernández-Cara - Mathematics of Control …, 2018 - Springer
This paper deals with the application of Stackelberg–Nash strategies to the null
controllability of degenerate parabolic equations. We assume that we can act on the system …

Carleman estimates and observability inequalities for parabolic equations with interior degeneracy

G Fragnelli, D Mugnai - Advances in Nonlinear Analysis, 2013 - degruyter.com
We consider a parabolic problem with degeneracy in the interior of the spatial domain, and
we focus on Carleman estimates for the associated adjoint problem. The novelty of interior …

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions

I Boutaayamou, G Fragnelli, L Maniar - Journal d'Analyse Mathématique, 2018 - Springer
We consider a parabolic problem with degeneracy in the interior of the spatial domain and
Neumann boundary conditions. In particular, we focus on the well-posedness of the problem …

Degenerate parabolic operators of Kolmogorov type with a geometric control condition

K Beauchard, B Helffer, R Henry… - … : Control, Optimisation and …, 2015 - numdam.org
We consider Kolmogorov-type equations on a rectangle domain (x, v)∈ Ω= T×(− 1, 1), that
combine diffusion in variable v and transport in variable x at speed vγ, γ∈ N*, with Dirichlet …

Boundary controllability for a 1D degenerate parabolic equation with drift and a singular potential

L Galo-Mendoza, M López-García - arxiv preprint arxiv:2302.01197, 2023 - arxiv.org
We prove the null controllability of a one dimensional degenerate parabolic equation with
drift and a singular potential. We study the case the potential arises at the left end point and …