ABSTRACT. In this paper, we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. We establish a local Carleman estimate for Biot consilidation system. Using this estimate, we prove the uniqueness and a Hölder stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects λ * and on the other hand the two spatially varying density by a single measurement of solution over ω × (0, T ), where T > 0 is a sufficiently large time and a suitable subbdomain ω satisfying ∂ω ⊃ ∂Ω.

In this paper, we study the global stability in determination of a coefficient in the transmission wave equation from data of the solution in a subboundary over a time interval. Providing regular initial data, we prove a hölder stability estimate in the inverse problem with a single measurement. Moreover, the exponent in the stability estimate depends on the regularity of initial data.

International audience Dans ce papier, on a prouvé une estimation de stabilité de type Höldérienne pour un problème inverse de détermination du terme source de l'équation de la chaleur à l'aide d'une inégalité de Carleman pour un système d'équations hyperbolique-parabolique couplé. ABSTRACT. In this paper we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. Using a local Carleman estimate for a coupled hyperbolic-parabolic system, we prove the uniqueness and a Hölder stability in determining the heat source by a single measurement of solution over ω × (0, T), where T > 0 is a sufficiently large time and a suitable subbdomain ω ⊂ Ω such that ∂ω ⊃ ∂Ω. MOTS-CLÉS : Problème inverse, estimation de Carleman, système couplet