## About

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## Publications

Publications (59)

Dehydration of the oceanic subducting slab promotes the formation of magmatic arcs, intra-slab intermediate-depth seismicity, and hydration of the overlying mantle wedge. However, the complex permeability structure of the overriding plate controls the magma and fluid migration and their accumulation at shallower depths. In this regard, mapping the...

In this work, we study a Lipschitz stability result in the reconstruction of a compactly supported initial temperature for the heat equation in $\mathbb{R}^n$, from measurements along a positive time interval and over an open set containing its support. We take advantage of the explicit dependency of solutions to the heat equation with respect to t...

We investigate the variations of the seismic source properties and aftershock activity using kinematic inversions and template-matching, for six large magnitude intermediate-depth earthquakes occurred in northern Chile. Results show similar rupture geometry and stress drop values between 7–30 MPa. Conversely, aftershocks productivity systematically...

We study an inverse problem for Light Sheet Fluorescence Microscopy (LSFM), where the density of fluorescent molecules needs to be reconstructed. Our first step is to present a mathematical model to describe the measurements obtained by an optic camera during an LSFM experiment. Two meaningful stages are considered: excitation and fluorescence. We...

Here we present an Algebraic Reconstruction Technique (ART) for solving the identification problem in Single Photon Emission Computed Tomography (SPECT). Traditional reconstruction for SPECT is done by finding the radiation source, nevertheless the attenuation of the surrounding tissue affects the data. In this context, ballistic and first scatteri...

Fixed points are fundamental states in any dynamical system. In the case of
gene regulatory networks (GRNs) they correspond to stable genes profiles
associated to the various cell types. We use Kauffman's approach to model GRNs
with random Boolean networks (RBNs). We start this paper by proving that, if we
fix the values of the source nodes (nodes...

Air quality networks need revision and optimisation as instruments and network requirements, both scientific and societal, evolve over time. Assessing and optimising the information content of a monitoring network is a non-trivial problem. Here, we introduce a methodology formulated in a variational framework using an air quality model to simulate...

High fidelity image synthesis is cornerstone to the cutting-edge science expected from ALMA. This involves turning an array of antennas spread over 16km, into an equivalent 16km-sized telescope, which is limited by atmospheric turbulence and in-homogeneous Fourier coverage. For optimal image quality the calibration of full ALMA data has to be boots...

In medical SPECT imaging, we seek to simultaneously obtain the internal
radioactive sources and the attenuation map using not only ballistic
measurements but also first order scattering measurements. The problem is
modeled using the radiative transfer equation by means of an explicit nonlinear
operator that gives the ballistic and scattering measur...

When describing the mechanical behaviour of the lithosphere modelled as a thin plate, the most important parameter corresponds to its flexural rigidity, which is commonly expressed through the effective elastic thickness, Te. This parameter is a measure of the stiffness of the plate and defines the maximum magnitude and wavelength of those surface...

We consider the inverse problem of determining the spatial dependence of the source term in a heat equation in assuming known, from a single internal measurements of the solution in . The purpose of this paper is to establish a reconstruction formula for similar to the one obtained by M. Yamamoto in "Stability, Reconstruction formula and regulariza...

Using uniform global Carleman estimates for discrete elliptic and
semi-discrete hyperbolic equations, we study Lipschitz and logarithmic
stability for the inverse problem of recovering a potential in a semi-discrete
wave equation, discretized by finite differences in a 2-d uniform mesh, from
boundary or internal measurements. The discrete stability...

One of the most studied inverse problems in cellular automata (CAs) is
the density classification problem. It consists in finding a CA such
that, given any initial configuration of 0s and 1s, it converges to the
all-1 fixed point configuration if the fraction of 1s is greater than
the critical density 1/2, and it converges to the all-0 fixed point...

In this paper, we consider two linear plate models, namely the Reissner–Mindlin system (R–M) and the Kirchhoff–Love equation (K–L), which come from linear elasticity. We prove global Carleman inequalities for both models with boundary observations and under a suitable hypothesis on the parameters. We use these estimates to study the inverse problem...

The rotated multipliers method is performed in the case of the boundary stabilization by means of a(linear or non-linear) Neumann feedback. this method leads to new geometrical cases concerning the "active" part of the boundary where the feedback is apllied. Due to mixed boundary conditions, these cases generate singularities. Under a simple geomet...

When constraining surface emissions of air pollutants using inverse modelling one often encounters spurious corrections to the inventory at places where emissions and observations are colocated, referred to here as the colocalization problem. Several approaches have been used to deal with this problem: coarsening the spatial resolution of emissions...

Data assimilation refers to any methodology that uses partial
observational data and the dynamics of a system for estimating the
model state or its parameters. We consider here a non classical
approach to data assimilation based in null controllability
introduced in [Puel, C. R. Math. Acad. Sci. Paris
335 (2002) 161–166] and [Puel, SIAM J. Control...

We proved a Carleman estimate and a sharp unique continuation result for the integro-differential hyperbolic system of the 3D viscoelasticity problem. We used these results to obtain a logarithmic stability estimate for the inverse problem of recovering the spatial part of a viscoelastic coefficient of the form p(x)h(t) from a unique measurement on...

The Chilean subduction zone presents a unique opportunity to study trench outer rise deformation of the subducting oceanic lithosphere at different thermal ages. The shape of the outer rise for plate ages ranging from 0 to 50 Ma is predicted by using an elastic plate model with variable elastic thickness Te(x) as a function of the distance measured...

We study the boundary stabilization of the wave equation by means of a linear or non-linear Neumann feedback. The rotated multiplier method leads to new geometrical cases concerning the active part of the boundary where the feedback is applied. Due to mixed boundary conditions, these cases generate singularities. Under a simple geometrical conditio...

In this Note, we prove a Carleman's estimate for the integro-differential hyperbolic system of the viscoelasticity problem and we use this estimate to obtain a stability result for the inverse problem of recovering a viscoelastic coefficient from a unique internal measure. To cite this article: M. de Buhan, A. Osses, C. R. Acad. Sci. Paris, Ser. I...

We consider the bistable equation vt−Δv=f(v,x), f(v,x)=a(x)v(1−v)(v−α(x)) with homogeneous Neumann boundary conditions in a bounded domain Ω⊂R3 with regular boundary. For this equation, we prove Lipschitz stability for the inverse problem of recovering parameters a and α from measurements of v in (0,T)×ω, where ω is an arbitrary nonempty open subse...

We study a non standard unique continuation property for the biharmonic spectral problem $\Delta^2 w=-\lambda\Delta w$ in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle $0<\theta_0<2\pi$, $\theta_0\not=\pi$ and $\theta_...

Emission inventories (EIs) are key-tools for air quality management. However, EIs are expensive, and they have uncertainties. A way to improve the accuracy of EIs is data assimilation. Multiple inverse methods have been used at various scales. However, typically, when applying these methods at the city scale, one encounters, in addition to 5 proble...

To allow the survival of the population in the absence of nitrogen, some cyanobacteria strains have developed the capability of differentiating into nitrogen fixing cells, forming a characteristic pattern. In this paper, the process by which cyanobacteria differentiates from vegetative cells into heterocysts in the absence of nitrogen and the eleme...

Undesirable splashing appears in copper converters when air is injected into the molten matte to trigger the conversion process. We consider here a cylindrical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid dynamics in a...

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- sch...

In this Note, we derive new Carleman inequalities for the evolution Schrodinger equation under a weak pseudoconvexity condition, which allows us to use weights with a linear spatial dependence. As a result, less restrictive boundary or internal observation regions may be used to obtain the stability for the inverse problem consisting in retrieving...

(Baudouin and Puel 2002 Inverse Problems 18 1537–54), investigated some inverse problems for the evolution Schrödinger equation by means of Carleman inequalities proved under a strict pseudoconvexity condition. We show here that new Carleman inequalities for the Schrödinger equation may be derived under a relaxed pseudoconvexity condition, which al...

We study the asymptotic behavior of a system modeling a composite material made of an elastic periodically perforated support, with period epsilon > 0, and a perfect gas placed in each of these perforations, as epsilon goes to zero. The model we use is linear, corresponding to deformations around a reference configuration. We apply both two-scale a...

In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given...

Travel-time inversion requires the computation of the arrival time derivative with re-spect to some given parameter of the unknown medium, such as velocities or depth-nodes. We consider here two different types of travel-time inversion: (1) assuming that the final point of the ray-path is constant and (2) assuming that the initial angle of the ray-...

Undesirable splashing appears in copper converters when air is injected into the molten matte in order to carry out the conversion process. We consider here a cylin- drical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid...

In this paper we prove an inverse inequality for the parabolic equation υt‒ ϵΔυ+M.∇υ=ƒ1ω with Dirichlet boundary conditions. With the motivation of finding an estimate of ƒ in terms on the trace of the solution in O×( 0, T ) for ϵ small ,our approach consists in studying the convergence of the solutions of this equation to the solutions of some tra...

We consider the two-dimensional motion of a rigid structure immersed in an incompressible fluid governed by Navier-Stokes equations. The control force acts on a fixed subset of the fluid domain. We prove that our system is null controllable; that is, for small initial data, the system can be driven at rest and the structure can be driven to the ori...

In this paper, we establish geometrical conditions in order to solve an inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data from a single time-dependent Neumann boundary measurement on a suitable part of the boundary. We prove the uniqueness and the stability results for this problem when a Neumann measure...

This paper reviews four variants of global Carleman weights that are especially adapted to some singular controllability and inverse problems in partial differential equations. These variants arise when studying: i) one measurement stationary source inverse problems for the heat equation with discontinuous coeffi cients, ii) one measurement station...

We establish geometrical conditions for the inverse problem of determining a stationary potential in the wave equation with Dirichlet data from a Neumann measurement on a suitable part of the boundary. We present the stability results when we measure on a part of the boundary satisfying a rotated exit condition. The proofs rely on global Carleman e...

We consider a linear quasi-geostrophic ocean model with partially known initial conditions. We search for controls that make the observation locally insensitive to the perturbations of the initial data. Their existence is equivalent to the null controllability property for an associated cascade Stokes-like system. Thanks to the presence of the Cori...

The L2- and H1-approximate controllability and homogenization of a semilinear elliptic boundary-value problem is studied in this paper. The principal term of the state equation has rapidly oscillating coefficients and the control region is locally distributed. The observation region is a subset of codimension 1 in the case of L2-approximate control...

We consider here a linear quasi-geostrophic ocean model. We look for controls insensitizing (resp. ε-insensitizing) an observation function of the state. The existence of such controls is equivalent to a null controllability property (resp. an approximate controllability property) for a cascade Stokes-like system. Under reasonable assumptions on th...

The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal...

A new family of multipliers with rotated direction is introduced. This technique is applied to obtain new results concerning controllability of waves, elasticity, and Stokes equations. The boundary exact controllability for the wave equation and the dynamic elasticity system is reviewed generalizing the classical exit condition in the case of expli...

We consider a control problem involving a semilinear elliptic equation with a uniformly Lipschitz non-linearity and rapidly oscillating coefficients in a bounded domain of $mathbb{R}^N$. The control is distributed on a compact subset interior to the domain. Given an $N-1$ dimensional hypersurface at the interior of the domain not intersecting the c...

An asymptotic study of two spectral models which appear in fluid-solid vibrations is presented in this paper. These two models are derived under the assumption that the fluid is slightly compressible or viscous respectively. In the first case, min-max estimations and a limit process in the variational formulation of the corresponding model are used...

We consider a linear model of interaction between a viscous incompressible
fluid and a thin elastic structure located on a part of the fluid domain
boundary, the other part being rigid. After having given an existence and
uniqueness result for the direct problem, we study the question of
approximate controllability for this system when the control...

Studying the possibility of controlling the movement of a viscous incompressible fluid by an action on the surrounding elastic structure is an important question. At the moment, the general problem involving Navier Stokes equations in domains varying with time, coupled with a nonlinear elastodynamic equation on the boundary is out of possibility.

We study the approximate controllability of a stationary Stokes system with linearized convection in a bounded domain of N. The control acts on a part of the boundary and the velocity field is observed on an interior curve (N=2) or surface (N=3). We establish the L
2-approximate controllability under certain compatibility conditions and suitable ge...

Two new choices in the multiplier method to study the exact controllability of the wave equation are introduced: a new family of multipliers with rotated direction and multipliers with multiple directions. New geometrical examples with explicit estimates of the observability constant are found.

The boundary approximate controllability of the Laplace equation observed on an interior curve is studied in this paper. First we consider the Laplace equation with a bounded potential. The L p (1<p<∞) approximate controllability is established and controls of L p -minimal norm are built by duality. At this point, a general result which clarifies t...

This paper is concerned with the added mass matrix for a mechanical structure vibrating in an incompressible liquid. It is shown in particular that this matrix does not depend on viscosity and, from this fact, can be calculated as if the fluid is perfect. The viscous effect on the mechanical system can then be represented by a damping term of type...

We study here two inverse problems for the Laplace equation and for a generalized Stokes system, using approximate controllability methods. This enables us to give constructive results. The method is then used to develop numerical algorithms. Numerical results are given for the case of Laplace equation.

## Projects

Project (1)