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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 Makridakis
Underground 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 Engineering

ISSN

1741-5977

Publisher

Taylor & Francis

Issue

5

Volume

21

Page range

823-839

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-02-06

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