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Control estimates and well-posedness of an inverse subsidence problem in geomechanics
journal contribution
posted on 2023-06-08, 19:58 authored by E Vairaktaris, Charalambos MakridakisCharalambos MakridakisUnderground geotechnical or civil engineering works change the primary stressed and strained state of the rock mass and subsequently the fields of displacement and stresses. A significant effect of these changes is the formation of subsidence in the earth's surface with significant negative economic or other consequences. In a series of recent works, large-scale subsidence in geostructures was modelled using Litwiniszyn's theory (Einstein-Kolmogorov Differential Equation) and the trap-door mechanism. The solution of the Inverse Subsidence Diffusion-Convection (ISDC) problem - which belongs to the class of backward parabolic problems - provides the base (gravity-directed) displacement using the surface subsidence as 'initial' condition. Early well-posedness of the initial and boundary value problems has already been examined (in terms of stability estimates) in previous papers. In this work, study of control estimates and well-posedness of the ISDC problem, using energy method, are discussed. © 2013 Copyright Taylor and Francis Group, LLC.
History
Publication status
- Published
Journal
Inverse Problems in Science and EngineeringISSN
1741-5977Publisher
Taylor & FrancisExternal DOI
Issue
5Volume
21Page range
823-839Department affiliated with
- Mathematics Publications
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- No
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- Yes
Legacy Posted Date
2015-02-06Usage metrics
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