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

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 consolidation 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 densities by a single measurement of solution over ω × (0,T), where T > 0 is a sufficiently large time and a suitable subdomain ω satisfying ∂ω⊃∂Ω. Copyright © 2016 John Wiley & Sons, Ltd.