Hoài-Minh Nguyên
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View article: On the local null controllability of a viscous Burgers' system in finite time
On the local null controllability of a viscous Burgers' system in finite time Open
This paper is devoted to the local null controllability of the Burgers control system $y_t - y_{xx} + y y_x = u(t)$ on a bounded interval imposed by the zero Dirichlet boundary condition. It is known from the work of Marbach that this cont…
View article: A short introduction to the control theory in finite-dimensional spaces
A short introduction to the control theory in finite-dimensional spaces Open
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Mathématiques et applications at Sorbonne University, delivered over the past few years. T…
View article: One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions
One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions Open
This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…
View article: PID TRAJECTORY TRACKING CONTROL FOR BALL-AND-PLATE SYSTEM
PID TRAJECTORY TRACKING CONTROL FOR BALL-AND-PLATE SYSTEM Open
Ball-on-Plate (BoP) is developing a ball-and-beam system. This transformation transforms a single input-multi output (SIMO) system into a multi input-multi output (MIMO) under-actuated system. In this paper, we utilize the PID method—a pop…
View article: One Dimensional Wave Equation with In-Domain Localized Damping and Wentzell Boundary Conditions
One Dimensional Wave Equation with In-Domain Localized Damping and Wentzell Boundary Conditions Open
View article: Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces for radial functions
Gagliardo–Nirenberg inequalities in fractional Coulomb–Sobolev spaces for radial functions Open
View article: Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions Open
This paper considers a one-dimensional wave equation on [0,1], with dynamic boundary conditions of second order at x=0 and x=1, also referred to as Wentzell/Ventzel boundary conditions in the literature. In additions the wave is subjected …
View article: Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation
Rapid stabilization and finite time stabilization of the bilinear Schrödinger equation Open
We propose a method to establish the rapid stabilization of the bilinear Schrödinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the rap…
View article: Lack of local controllability for a water-tank system when the time is not large enough
Lack of local controllability for a water-tank system when the time is not large enough Open
We consider the small-time local-controllability property of a water tank modeled by one-dimensional Saint-Venant equations, where the control is the acceleration of the tank. It is known from the work of Dubois et al. that the linearized …
View article: Stabilization of control systems associated with a strongly continuous group
Stabilization of control systems associated with a strongly continuous group Open
This paper is devoted to the stabilization of a linear control system $y' = A y + B u$ and its suitable non-linear variants where $(A, \cD(A))$ is an infinitesimal generator of a strongly continuous {\it group} in a Hilbert space $\mH$, an…
View article: Exponential Decay of Solutions of Damped Wave Equations in One Dimensional Space in the <i>L</i><sup>p</sup> Framework for Various Boundary Conditions
Exponential Decay of Solutions of Damped Wave Equations in One Dimensional Space in the <i>L</i><sup>p</sup> Framework for Various Boundary Conditions Open
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based …
View article: The Caffarelli–Kohn–Nirenberg inequalities for radial functions
The Caffarelli–Kohn–Nirenberg inequalities for radial functions Open
We establish the full range of the Caffarelli–Kohn–Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order . In particular, we show that the range of the parameters for radial functions is stri…
View article: The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions
The Weyl Law of Transmission Eigenvalues and the Completeness of Generalized Transmission Eigenfunctions without Complementing Conditions Open
The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the g…
View article: Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions
Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions Open
We establish the exponential decay of the solutions of the damped wave equations in one-dimensional space where the damping coefficient is a nowhere-vanishing function of space. The considered PDE is associated with several dynamic boundar…
View article: Local controllability of the Korteweg-de Vries equation with the right Dirichlet control
Local controllability of the Korteweg-de Vries equation with the right Dirichlet control Open
The Korteweg-de Vries (KdV) equation with the right Dirichlet control was initially investigated more than twenty years ago. It was shown that this system is small time, locally, exactly controllable for all non-critical lengths and its li…
View article: The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions without complementing conditions
The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions without complementing conditions Open
The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the g…
View article: On the small-time local controllability of a KdV system for critical lengths
On the small-time local controllability of a KdV system for critical lengths Open
This paper is devoted to the local null-controllability of the nonlinear KdV equation equipped the Dirichlet boundary conditions using the Neumann boundary control on the right. Rosier proved that this KdV system is small-time locally cont…
View article: Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions
Exponential decay of solutions of damped wave equations in one dimensional space in the $L^p$ framework for various boundary conditions Open
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based …
View article: Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems
Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems Open
Hyperbolic systems in one-dimensional space are frequently used in the modeling of many physical systems. In our recent works we introduced time-independent feedbacks leading to finite stabilization in optimal time of homogeneous linear an…
View article: Cloaking Property of a Plasmonic Structure in Doubly Complementary Media and Three-Sphere Inequalities with Partial Data
Cloaking Property of a Plasmonic Structure in Doubly Complementary Media and Three-Sphere Inequalities with Partial Data Open
International audience
View article: A Dependence of the Cost of Fast Controls for the Heat Equation on the Support of Initial Datum
A Dependence of the Cost of Fast Controls for the Heat Equation on the Support of Initial Datum Open
International audience
View article: The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations Open
View article: Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces
Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces Open
We establish the full range Gagliardo-Nirenberg and the Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces for the (fractional) derivative $0 \leq s \leq 1$. As a result, we rediscover known Gaglair…
View article: The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations Open
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission problem and studied their locations. In this pap…
View article: The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions
The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions Open
View article: Decay for the nonlinear KdV equations at critical lengths
Decay for the nonlinear KdV equations at critical lengths Open
View article: Data for: Non-local, non-convex functionals converging to Sobolev norms
Data for: Non-local, non-convex functionals converging to Sobolev norms Open
We study the pointwise convergence and the $\Gamma$-convergence of a family of non-local, non-convex functionals $\Lambda_\delta$ in $L^p(\Omega)$ for $p>1$. We show that the limits are multiples of $\int_{\Omega} |\nabla u|^p$. This is a …
View article: On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients
On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients Open
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear hyp…
View article: A dependence of the cost of fast controls for the heat equation on the support of initial datum
A dependence of the cost of fast controls for the heat equation on the support of initial datum Open
The controllability cost for the heat equation as the control time $T$ goes to 0 is well-known of the order $e^{C/T}$ for some positive constant $C$, depending on the controlled domain and for all initial datum. In this paper, we prove tha…
View article: Null-controllability of linear hyperbolic systems in one dimensional space
Null-controllability of linear hyperbolic systems in one dimensional space Open