Carleman estimate for Biot consolidation system in poro‐elasticity and application to inverse problems. (16th June 2016)

• Record Type: Journal Article
• Authors: Bellassoued, Mourad; Riahi, Bochra
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 18(2016:Dec. 15)
• Page Start: 5281
• Page End: 5301
• Publication Date: 2016-06-16
• Subjects: Carleman estimates -- inverse problems -- Biot system; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3914
• Languages: English
• ISSNs: 0170-4214

Abstract

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.