Carleman estimate for Biot consolidation system in poro-elasticity and application to inverse problems

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 H\"older stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects $\lambda^*$ and on the other hand the two spatially varying density by a single measurement of solution over $\omega \times (0, T)$, where $T>0$ is a sufficiently large time and a suitable subbdomain $\omega$ satisfying $\p \omega \supset \p \Omega$.