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 consolidation system. Using this estimate, we prove the uniqueness and a Holder stability in determining on the one hand a physical parameter arising in connection with secondary consolidation effects and on the other hand the two spatially varying densities by a single measurement of solution over x (0,T), where T > 0 is a sufficiently large time and a suitable subdomain satisfying . Copyright (c) 2016 John Wiley & Sons, Ltd.