Nicolae Cindea

Université Clermont Auvergne | Univ BPC · Laboratoire de Mathématiques Blaise Pascal (LMBP)

The aim of this paper is to study the null controllability of a large class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately null controllable by the means of regular controls and that these controls depend continuously to the diffu...

The aim of this paper is to study the boundary controllability of the linear elasticity system as a first-order system in both space and time. Using the observability inequality known for the usual second-order elasticity system, we deduce an equivalent observability inequality for the associated first-order system. Then, the control of minimal \be...

The aim of this paper is to study the existence of weak solutions and of a finite stopping time for a large class of generalized newtonian fluids with thixotropic and shear-thinning flows. In a first time, the existence of the weak solutions is established using variational inequalities. In order to prove the existence of solutions we regularize th...

This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro, C\^indea and M\"unch in SIAM J. Control Optim., 52 (2014) for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing t...

We consider a contact model with power-law friction in the antiplane context. Our study focuses on the boundary optimal control, paying special attention to optimality conditions and computational methods. Depending on the exponent of the power-law friction, we are able to deduce an optimality condition for the original problem or for a regularized...

This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cîndea-Münch, Controllability of the linear one-dimensional wave equation with inner moving forces, SIAM J. Control Optim 2014] for domains satisfying the usual...

This work is concerned with the distributed controllability of the one-dimensional wave equation over non-cylindrical domains. The controllability in that case has been obtained in [Castro-Cindea-Munch, Controllability of the linear one-dimensional wave equation with inner moving forces, SIAM J. Control Optim 2014] for domains satisfying the usual...

The aim of this paper is to propose a method to model and numerically simulate the inertial migration of particles in three-dimensional channels. The initial problem, coupling Navier–Stokes equations to the equations modeling the displacement of a spherical particle immersed in the fluid, is replaced by a first order expansion with respect to a sma...

Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is...

This article deals with the boundary observability and controllability properties of a space finite-differences semi-discretization of the clamped beam equation. We make a detailed spectral analysis of the system and, by combining numerical estimates with asymptotic expansions, we localize all the eigenvalues of the corresponding discrete operator...

The aim of this paper is to prove a uniform observability inequality for a finite differences semi-discretization of a clamped beam equation. A discrete multiplier method is employed in order to obtain the uniform observability of the eigenvectors of the matrix driving the semi-discrete system, corresponding to eigenfrequencies smaller than a preci...

We introduce a direct method that makes it possible to solve numerically inverse type problems for linear hyperbolic equations posed in − Ω, a bounded subset of . We consider the simultaneous reconstruction of both the state and the source term from a partial boundary observation. We employ a least-squares technique and minimize the L ²-norm of the...

The aim of this paper is to prove a uniform observability inequality for a finite differences semi-discretization of a clamped beam equation. A discrete multiplier method is employed in order to obtain the uniform observability of the eigenvectors of the matrix driving the semi-discrete system, corresponding to eigenfrequencies smaller than a preci...

We propose a sequential data assimilation scheme using Luenberger type observers when only some space restricted time under-sampled measurements are available. More precisely, we consider a wave-like equation for which we assume known the restriction of the solution to an open non-empty subset of the spatial domain and for some time samples (typica...

We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a bounded subset of $\mathbb{R}^N$ - from a partial boundary observation. We employ a least-squares technique and mi...

In this paper we study, from a control theoretic view point, a 1D model of fluid-particle interaction. More precisely, we consider a point mass moving in a pipe filled with a fluid. The fluid is modelled by the viscous Burgers equation whereas the point mass obeys Newton's second law. The control variable is a force acting on the mass point. The ma...

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a bounded subset of $\mathbb{R}^N$ - from a partial distributed observation. We employ a least-squa...

The aim of this work is to study of the numerical approximation of the controls for the hinged beam equation. A consequence of the numerical spurious high frequencies is the lack of the uniform controllability property of the semi-discrete model for the beam equation, in the classical setting. We solve this deficiency by adding a vanishing numerica...

This paper deals with the numerical computation of null controls for the wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [Cîndea, Fernández-Cara & Münch, Numerical controllability of the wave equation through...

This paper deals with the numerical computation of distributed null controls for the 1D wave equation. We consider supports of the controls that may vary with respect to the time variable. The goal is to compute approximations of such controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. As...

In this paper we summarize some recent results concerning the controllability of a one dimensional fluid-structure model. These results are confirmed by numerical experiments in some particular cases. More precisely, we consider a simplified model for a point swimmer moving, according to Newton's law, in an one dimensional fluid which is modeled by...

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not use in this work duality arguments but explore instead a direct app...

This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force $f$ . These approximations are obtained by combining a fixed point algorithm with the Galerkin method. It is known that the energy of the usual discrete models does not decay unif...

We propose an observer-based approach to circumvent the issue of unbounded approximation errors — with respect to the length of the time window considered — in the discretization of wave-like equations in bounded domains, which covers the cases of the wave equation per se and of linear elasticity as well as beam, plate and shell formulations, and s...

We analyze an observer strategy based on partial—that is, in a subdomain—measurements of the solution of a wave equation, in order to compensate for uncertain initial conditions. We prove the exponential convergence of this observer under a nonstandard observability condition, whereas using measurements of the time derivative of the solution would...

We consider the motion of a stretched string coupled with a rigid body at one end and we study the existence of periodic solution when a periodic force $f$ acts on the body. The main difficulty of the study is related to the weak dissipation that characterizes this hybrid system, which does not ensure a uniform decay rate of the energy. Under addit...

In this paper we study a controllability problem for a simplified 1-d nonlinear system which models the self-propelled motion of a rigid body in a fluid located on the real axis. The control variable is the difference of the velocities of the fluid and the solid and depends only on time. The main result of the paper asserts that any final positi...

We propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator. The algorithm combines Russell's ``stabilizability implies controllability" principle with the Galerkin's method. The main new feature brought in by this work consists in giving precise error estimates. In order...

In this work we prove that the exact internal observability for theEuler-Bernoulli equation is robust with respect to a class of linear perturbations. Our results yield,in particular,that for rectangular domains we have the exact observability in an arbitrarily small time and with an arbitrarily small observation region. The usual method of tacklin...

Electroporation consists in increasing the permeability of a tissue by applying high voltage pulses. In this paper we discuss the question of optimal placement and optimal loading of electrodes such that electroporation holds only in a given open set of the domain. The electroporated set of the domain is where the norm of the electric field is abov...

The aim of this thesis is to study, from a theoretical point of view, the exact controllability of some partial differential equations modeling the vibrations of an elastic structure and to apply the to apply these theoretic results to solve some inverse problems coming from magnetic resonance imaging (MRI). This thesis has two parts. The first one...

The aim of this thesis is to study the exact controllability and exact observability of some partial differential equations, modeling elastic vibrations of structures and to apply the results obtained in this way to solve some inverse problems provided by magnetic resonance imaging (MRI). This thesis has two parts. In the first part we study the ex...

The aim of this work is to study the exact observability of a perturbed plate equation. A fast and strongly localized observation result was proven using a perturbation argument of an Euler-bernoulli plate equation and a unique continuation result for bi-Laplacian.

We study the exact controllability of a nonlinear plate equation by the means of a control which acts on an internal region of the plate. The main result asserts that this system is locally exactly controllable if the associated linear Euler–Bernoulli system is exactly controllable. In particular, for rectangular domains, we obtain that the Berger...

This paper describes a rigorous framework for reconstructing MR images of the heart, acquired continuously over the cardiac and respiratory cycle. The framework generalizes existing techniques, commonly referred to as retrospective gating, and is based on the properties of reproducing kernel Hilbert spaces. The reconstruction problem is formulated...

Objectifs Présenter une méthode de reconstruction généralisée d’images IRM permettant de corriger les erreurs d’encodage spatial induites par le mouvement, à l’aide d’un modèle de déformations non-rigide s’appuyant sur des données physiologiques. Matériels et méthodes Des images d’une plate-forme de test comprenant un fantôme immobile et un mobile...

This article describes a general framework for multiple coil MRI reconstruction in the presence of elastic physiological motion. On the assumption that motion is known or can be predicted, it is shown that the reconstruction problem is equivalent to solving an integral equation--known in the literature as a Fredholm equation of the first kind--with...