Control estimates and well-posedness of an inverse subsidence problem in geomechanics

Vairaktaris, E and Makridakis, C (2013) Control estimates and well-posedness of an inverse subsidence problem in geomechanics. Inverse Problems in Science and Engineering, 21 (5). pp. 823-839. ISSN 1741-5977

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Catrina Hey
Date Deposited: 06 Feb 2015 12:07
Last Modified: 06 Feb 2015 12:08
URI: http://sro.sussex.ac.uk/id/eprint/52824
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