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

TL;DR

This paper develops a Carleman estimate for the Biot consolidation system in poro-elasticity, enabling the proof of uniqueness and stability in inverse problems involving physical parameters and densities from limited measurements.

Contribution

It introduces a new Carleman estimate for the coupled hyperbolic-parabolic Biot system and applies it to establish inverse problem results for parameter and density identification.

Findings

Proved a local Carleman estimate for the Biot system.

Established uniqueness in determining physical parameters and densities.

Achieved H"older stability in inverse problems from partial measurements.

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 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 $\p \omega \supset \p \Omega$.