Identifiabilité d'un coefficient variable en espace dans une équation parabolique
Identifiability and stability of boundaries in a supercritical free surface flow.
Identifiability for a class of discretized linear partial differential algebraic equations.
Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees.
We consider the inverse problem of determining point wave sources in heteregeneous trees, extensions of one-dimensional stratified sets. We show that the Neumann boundary observation on a part of the lateral boundary determines uniquely the point sources if the time of observation is large enough. We further establish a conditional stability and give a reconstructing scheme.
Identifiability, stability and reconstruction results of sources by interior measurements.
Identification and estimation of parameters in abstract Cauchy problems.
Identification de paramètres dans les problèmes non linéaires à données incomplètes
Identification of a localized source in an interstellar cloud: an inverse problem
We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position of a localized source , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation to the exact solution . By using semigroup theory, we prove existence and uniqueness...
Identification of a wave equation generated by a string
We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of cracks with non linear impedances
We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.
Identification of Green’s Functions Singularities by Cross Correlation of Ambient Noise Signals
In this paper we consider the problem of estimating the singular support of the Green’s function of the wave equation by using ambient noise signals recorded by passive sensors. We assume that noise sources emit stationary random signals into the medium which are recorded by sensors. We explain how the cross correlation of the signals recorded by two sensors is related to the Green’s function between the sensors. By looking at the singular support of the cross correlation we can obtain an estimate...
Identification of nonlinear coefficient in a transport equation.
Identification of source term in a nonlinear degenerate parabolic equation with memory
In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness...
Identification problems for degenerate parabolic equations
This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...
Intertwining methods in the problem of inverse scattering
Inverse boundary value problems for partial differential equations.
Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization
We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization
We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
Inverse parabolic problems and discrete orthogonality.