A lemma and a conjecture on the cost of rearrangements
A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems.
A quasi-boundary value method for regularizing nonlinear ill-posed problems.
A stability result in the localization of cavities in a thermic conducting medium
We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium in , , from a single pair of boundary measurements of temperature and thermal flux.
A stability result in the localization of cavities in a thermic conducting medium
We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium Ω in , n ≥ 2, from a single pair of boundary measurements of temperature and thermal flux.
A unique continuation theorem for the wave equation in the exterior of a characteristic cone
A uniqueness result in the theory of stereo vision : coupling shape from shading and binocular information allows unambiguous depth reconstruction
A wavelet Galerkin method applied to partial differential equations with variable coefficients.
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces...
An example of the absence of a global solution to some inverse problem for a hyperbolic equation.
An ill posed Cauchy problem for a hyperbolic system in two space dimensions
An ill-posed nonlocal two-point problem for systems of partial differential equations.
An inverse problem for Helmholtz's equation.
Application of He's homotopy perturbation method for Cauchy problem of ill-posed nonlinear diffusion equation.
Attracteurs compacts pour des problèmes d'évolution sans unicité
Boundary trace of solutions of semilinear elliptic equalities and inequalities
The boundary trace problem for positive solutions of is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over , where is a sufficiently large time interval and a subdomain satisfies a non-trapping condition.
Carleman estimates for the non-stationary Lamé system and the application to an inverse problem
In this paper, we establish Carleman estimates for the two dimensional isotropic non-stationary Lamé system with the zero Dirichlet boundary conditions. Using this estimate, we prove the uniqueness and the stability in determining spatially varying density and two Lamé coefficients by a single measurement of solution over (0,T) x ω, where T > 0 is a sufficiently large time interval and a subdomain ω satisfies a non-trapping condition.
Continuous dependence of solutions of some inverse problems in heat conduction
Continuous dependence on modeling for some well-posed perturbations of the backward heat equation.