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Logarithmic stability of an inverse problem for Biot’s consolidation system in poro-elasticity
Author(s) -
Wensheng Zhang,
Zifan Jiang
Publication year - 2019
Publication title -
journal of physics communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.407
H-Index - 17
ISSN - 2399-6528
DOI - 10.1088/2399-6528/ab596d
Subject(s) - biot number , logarithm , consolidation (business) , mathematics , mathematical analysis , elasticity (physics) , inverse , inverse problem , boundary value problem , physics , geometry , mechanics , thermodynamics , accounting , business
In this paper, we consider a coupled system of mixed hyperbolic-parabolic type, which describes Biot’s consolidation model in poro-elasticity. We study an inverse problem of determining five spatially varying coefficients in the model, i.e. two Lamé coefficients, the secondary consolidation effects and two densities, by three measurements of displacement in an arbitrary subboundary and temperature in an arbitrary neighborhood of the boundary over a time interval. By assuming that, in a neighborhood of the boundary of the spatial domain, the densities, secondary consolidation effects and the Lamé coefficients are known, we prove a logarithmic stability estimate for the inverse problem.

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