Jérémi Dardé

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This work considers the Cauchy problem for a second order elliptic operator in a bounded domain. A new quasi-reversibility approach is introduced for approximating the solution of the ill-posed Cauchy problem in a regularized manner. The method is based on a well-posed mixed variational problem on H1 × Hdiv with the corresponding solution pair converging(More)
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with Lipschitz boundary. It completes the results obtained in [4] for domains of class C. This estimate is established by using an interior Carleman estimate and a technique based on a sequence of balls which approach the(More)
In this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some(More)
We study the iterated quasi-reversibility method to regularize illposed elliptic and parabolic problems: data completion problems for Poisson’s and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data.(More)
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