Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions
M González-Burgos, L Ouaili - arXiv preprint arXiv:2401.17128, 2024 - arxiv.org
The general goal of this work is to obtain upper and lower bounds for the $ L^ 2$-norm of
biorthogonal families to complex exponential functions associated to sequences …
biorthogonal families to complex exponential functions associated to sequences …
A non-controllability result for the half-heat equation on the whole line based on the prolate spheroidal wave functions and its application to the Grushin equation
P Lissy - 2022 - hal.science
In this article, we revisit a result by A. Koenig concerning the non-controllability of the half-
heat equation posed on R, with a control domain that is an open set whose exterior contains …
heat equation posed on R, with a control domain that is an open set whose exterior contains …
Quantitative spectral inequalities for the anisotropic Shubin operators and applications to null-controllability
P Alphonse, A Seelmann - arXiv preprint arXiv:2212.10842, 2022 - arxiv.org
We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the
whole Euclidean space, thus relating for functions from spectral subspaces associated to …
whole Euclidean space, thus relating for functions from spectral subspaces associated to …
Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets
We consider the null-controllability problem for the generalized Baouendi-Grushin equation
$(\partial_t-\partial_x^ 2-q (x)^ 2\partial_y^ 2) f= 1_\omega u $ on a rectangular domain …
$(\partial_t-\partial_x^ 2-q (x)^ 2\partial_y^ 2) f= 1_\omega u $ on a rectangular domain …
Null-controllability of the Generalized Baouendi-Grushin heat like equations
In this article, we prove null-controllability results for the heat equation associated
tofractional Baouendi-Grushin operators $$\partial_t u+\bigl (-\Delta_x-V (x)\Delta_y\bigr) …
tofractional Baouendi-Grushin operators $$\partial_t u+\bigl (-\Delta_x-V (x)\Delta_y\bigr) …
On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories
In this work we analyse the small-time reachability properties of a nonlinear parabolic
equation, by means of a bilinear control, posed on a torus of arbitrary dimension $ d …
equation, by means of a bilinear control, posed on a torus of arbitrary dimension $ d …
[PDF][PDF] Quantitative spectral inequalities for the anisotropic Shubin operators and the Grushin operator
P Alphonse, A Seelmann - arXiv preprint arXiv:2212.10842, 2022 - hal.science
We prove quantitative spectral inequalities for the (anisotropic) Shubin operators and the
Grushin operator on the whole Euclidean space, thus relating for functions from spectral …
Grushin operator on the whole Euclidean space, thus relating for functions from spectral …
Unique continuation estimates for Baouendi--Grushin equations on cylinders
P Alphonse, A Seelmann - arXiv preprint arXiv:2401.17782, 2024 - arxiv.org
We prove time-pointwise quantitative unique continuation estimates for the evolution
operators associated to (fractional powers of) the Baouendi--Grushin operators on the …
operators associated to (fractional powers of) the Baouendi--Grushin operators on the …
Exact controllability to eigensolutions of the heat equation via bilinear controls on two-dimensional domains
R Buffe, A Duca - arXiv preprint arXiv:2406.17348, 2024 - arxiv.org
The exact controllability of heat type equations in the presence of bilinear controls have
been successfully studied in the recent works [1, 3, 14] motivated by the numerous …
been successfully studied in the recent works [1, 3, 14] motivated by the numerous …
Critical time for the observability of Kolmogorov-type equations
This paper is devoted to the observability of a class of two-dimensional Kolmogorov-type
equations presenting a quadratic degeneracy. We give lower and upper bounds for the …
equations presenting a quadratic degeneracy. We give lower and upper bounds for the …