Emmanuelle Crepeau

Emmanuelle Crepeau
Université de Versailles Saint-Quentin | UVSQ · Département des Mathématiques

PhD

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40
Publications
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744
Citations

Publications

Publications (40)
Article
Full-text available
In this work, we deal with the exponential stability of the nonlinear Korteweg–de Vries equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then, we state an exponential stabilization result using a Lyapunov function by imposing smal...
Article
Full-text available
The generalized Hirota-Satsuma system consists of three coupled nonlinear Korteweg-de Vries (KdV) equations. By using two distributed controls it is proven in this paper that the local null controllability property holds when the system is posed on a bounded interval. First, the system is linearized around the origin obtaining two decoupled subsyst...
Article
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A system of |$N$| Korteweg–de Vries equations coupled by the boundary conditions is considered in this paper. The configuration studied here is the one called star-shaped network, where the boundary inputs can act on a central node and on the |$N$| external nodes. In the literature, there is a recent result proving the exact controllability of this...
Preprint
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The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimen...
Article
Full-text available
We study the stabilization issue of the Benjamin-Bona-Mahony (BBM) equation on a finite star-shaped network with a damping term acting on the central node. In a first time, we prove the well-posedness of this system. Then thanks to the frequency domain method, we get the asymptotic stabilization result.
Article
Full-text available
The improved Boussinesq equation is studied in this paper. Control properties for this equation posed on a bounded interval are first considered. When the control acts through the Dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable. In a second part, the equation is posed on the one-dimen...
Article
This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional system is well-posed for small initial data. The main results of our study are two theorems stating the exponent...
Article
Full-text available
We propose a model using the Korteweg-de Vries $(KdV)$ equation on a finite star-shaped network. We first prove the well-posedness of the system and give some regularity results. Then we prove that the energy of the solutions of the dissipative system decays exponentially to zero when the time tends to infinity. Lastly we show an exact boundary con...
Article
This article proposes some interface conditions for a Korteweg–de Vries (KdV) equation with a piecewise constant main coefficient. The well-posedness of the Cauchy problem is proved by using multiplier technique and then an observability inequality for the adjoint problem is obtained. We end up this article with a result of local exact controllabil...
Article
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This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg-de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhge. im-Klibanov method.
Article
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In this article, we present an inverse problem for the nonlinear 1D Kuramoto-Sivashinsky (KS) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability...
Article
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This study introduces a new signal analysis method called SCSA, based on a semi-classical approach. The main idea in the SCSA is to interpret a pulse-shaped signal as a potential of a Schr\"odinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results...
Article
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We are interested in an inverse problem for the wave equation with potential on a starshaped network. We prove the Lipschitz stability of the inverse problem consisting in the determination of the potential on each string of the network with Neumann boundary measurements at all but one external vertices. Our main tool, proved in this article, is a...
Article
This paper concerns the nonlinear 1D FitzHugh Nagumo system with a Robin bound-ary control. We prove that this system is "flat-like" with the outflow electrical potential playing the role of the flat output. Indeed, the solution can be expressed in terms of an infinite series depending on the derivatives and the integrals of the flat output. This s...
Article
Dans cet exposé, je présenterai une nouvelle méthode d'analyse de signaux basée sur une approche semi-classique appelée SCSA. L'idée principale de la SCSA consiste à interpréter un signal en forme d'impulsions comme un potentiel de l'opérateur de Schrödinger et à utiliser le spectre discret de cet opérateur pour la reconstruction et l'analyse du si...
Conference Paper
Full-text available
This article introduces a new signal analysis method. The main idea consists in interpreting a pulse-shaped signal, after multiplying it by a positive parameter, as a potential of a Schr\"odinger operator and representing this signal with the discrete spectrum of this operator. We present some results obtained in the analysis of the arterial blood...
Article
Full-text available
We consider a control system for a Korteweg-de Vries equation with homogeneous Dirichlet boundary conditions and Neumann boundary control. We address the rapid exponential stabilization problem. More precisely, we build some feedback laws forcing the solutions of the closed-loop system to decay exponentially to zero with arbitrarily prescribed deca...
Article
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It is known that the linear Korteweg-de Vries (KdV) equation with homogeneous Dirichlet boundary conditions and Neumann boundary control is not controllable for some critical spatial domains. In this paper, we prove in these critical cases, that the nonlinear KdV equation is locally controllable around the origin provided that the time of control i...
Article
An open-loop control for a system coupling a reaction-diffusion system and an ordinary differential equation is proposed in this study. We use a flatness-like property, indeed, the solution can be expressed in terms of an infinite series depending on a flat output, its derivatives and its integrals. This series is shown to be convergent if the flat...
Conference Paper
A parsimonious representation of signals is a mathematic model parametrized with a small number of parameters. Such models are useful for analysis, interpolation, filtering, feature extraction, and data compression. A new parsimonious model is presented in this paper based on scattering transforms. It is closely related to the eigenvalues and eigen...
Conference Paper
Full-text available
We propose in this work a computational method for approximating signed functions using only the discrete spectrum of a one dimensional Schrodinger operator. The method is based on the scattering transform of the Schrodinger operator and denoted SBSA (Scattering Based Signal Analysis). The scattering transform is a nonlinear transformation analogou...
Article
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A new method for analyzing arterial blood pressure is presented in this article. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which...
Article
In this article we propose a reduced model of the input–output behaviour of an arterial compartment, including the short systolic phase where wave phenomena are predominant. The objective is to provide basis for model-based signal processing methods for the estimation from non-invasive measurements and the interpretation of the characteristics of t...
Article
A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave which describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow that represents the slow phenomena d...
Article
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This article presents a new travelling waves ana-lysis and identification method based on scattering theory. This inverse scattering technique consists on solving the spectral problem associated to a one-dimensional Schrodinger operator perturbed by a potential depending upon the wave to analyze, and optimized in order to approximate this wave by a...
Article
Full-text available
This article presents a new method for analyzing arterial blood pressure waves. The technique is based on the scattering transform and consists in solving the spectral problem associated to a one-dimensional Schrödinger operator with a potential depending linearly upon the pressure. This potential is then expressed with the discrete spectrum which...
Article
Full-text available
We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate...
Conference Paper
Full-text available
In this article we propose a reduced model of the input-output behaviour of an arterial compartment, including the short systolic phase where wave phenomena are predominant. The objective is to provide basis for model-based signal processing methods for the estimation from non-invasive measurements and the interpretation of the characteristics of t...
Article
A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow represents the slow phenomena during the d...
Article
Full-text available
De nos jours, le concept de tension artérielle, qui fait référence à la pression artérielle (PA), devient de plus en plus familier et intègre le langage courant. Ceci est dû à l'incidence de la mortalité due aux maladies cardio-vasculaires et en raison du rôle fondamental que joue la PA dans l'appareil circulatoire. L'intérêt porté à la PA a mobili...
Article
Full-text available
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin...
Article
Full-text available
The purpose of this article is to study the exact boundary controllability of the classical Boussinesq equation. The control is applied to the first spatial derivative and then, to the second spatial derivative, both at the right endpoint. The exact controllability of the linearized problem is essentially proved by using the Hilbert Uniqueness Meth...
Article
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Puel Jean-Pierre, président du jury; Raymond Jean-Pierre, Rouchon pierre, Tucsnak Marius, membres du jury;
Article
Full-text available
The exact boundary controllability of the non-linear Korteweg-de Vries equation on bounded domains is studied. Only the first spatial derivative at the right endpoint is assumed to be controlled. In this case, the exact controllability has been shown by Rosier (1997) when the length L of the domain is not in the set N:= {2 pi root (k(2) + kl +l(2))...
Article
Full-text available
Abstract In this work, we aim at giving a reduced arterial blood pressure (ABP) model that is composed of a nonlinear superposition of for- ward solitary waves completed by a windkessel flow. The former takes into account fast phenomena which predominate during the systolic phase and the latter represents slow phenomena during the diastolic phase....

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