arXiv subjects

Rémi Buffe

Publications and source records attributed to Rémi Buffe.

6 recordsLinked to original sources

arXiv2026

Bilinear controllability for the linear KdV-Schr{ö}dinger equation

We study the controllability of a linear KdV-Schr{ö}dinger equation on the one-dimensional torus via purely imaginary bilinear controls. Considering controls spanning a suitable finite number of Fourier modes, we prove small-time global approximate controllability in L2(T). The result holds between any pair of states with the same norm and is obtained via the saturation method by following the idea introduced in [Poz24]. We first establish small-time controllability for phase multiplications, and then generate transport operators associated with diffeomorphisms of the torus. Finally, we combine these results to recover global approximate controllability. Note that the controllability property holds independently of the Schr{ö}dinger component of the dynamics, which may in particular be taken to vanish.

eess.SY↗

arXiv2026

Small-time estimates for a real moment problem with two-term Weyl spectral law

In this work, we first study the solvability of moment problems involving real exponentials and provide explicit estimates of the associated control cost. The result holds when the increasing sequence of distinct real numbers satisfies a suitable two-term Weyl asymptotic law, without imposing any uniform spacing condition on blocks of its elements. We then deduce a corresponding controllability result for a linear control problem. Next, we present an exponential family fitting our hypotheses that cannot be treated by existing results of this type. Finally, we show how to deduce new exact controllability results for suitable fractional bilinear heat equations in higher-dimensional domains.

math.AP↗

arXiv2023

An optimal spectral inequality for degenerate operators

In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerate one dimensional elliptic operator. Carleman techniques and moment method are combined. Application to null controllability on a measurable set in time for the degenerated heat equation is described.

math.AP↗

arXiv2021

Controllability of a simplified fluid-structure interaction system

We are interested by the controllability of a fluid-structure interaction system where the fluid is viscous and incompressible and where the structure is elastic and located on a part of the boundary of the fluid's domain. In this article, we simplify this system by considering a linearization and by replacing the wave/plate equation for the structure by a heat equation. We show that the corresponding system coupling the Stokes equations with a heat equation at its boundary is null-controllable. The proof is based on Carleman estimates and interpolation inequalities. One of the Carleman estimates corresponds to the case of Ventcel boundary conditions. This work can be seen as a first step to handle the real system where the structure is modeled by the wave or the plate equation.

math.AP↗

arXiv2021

Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity

We prove an inequality of Hölder type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness by a global approach using a refined parabolic frequency function method. It relies with a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.

math.AP↗

arXiv2018

A spectral inequality for degenerated operators and applications

In this paper we establish a Lebeau-Robbiano spectral inequality for a degenerated one dimensional elliptic operator and show how it can be used to impulse control and finite time stabilization for a degenerated parabolic equation. R{é}sum{é} .-Dans cet article, on s'int{é}r{è}ss{è} a l'in{é}galit{é} spectrale de type Lebeau-Robbiano sur la somme de fonctions propres pour une famille d'op{é}rateurs d{é}g{é}n{é}r{é}s. Les applications sont donn{é}es en th{é}orie du contr{ô}le comme le contr{ô}le impulsionnel et la stabilisation en temps fini.

math.AP↗