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Theses

Problèmes inverses et simulations numériques en viscoélasticité 3D.

Abstract : In this thesis, we considered various mathematical and numerical problems related to the system of viscoelasticity in three dimensions. In the first part, we focused on the linear system and more specifically on the inverse problem of recovering a viscoelastic coefficient. For this system, we proved a Carleman estimate (Chapter 1) and a stability result in the unique continuation (Chapter 2). We used these results to establish two stability estimates for the inverse problem, the first one related to a unique internal measurement and the second to a unique measurement on an arbitrarily small part of the boundary (Chapter 3). Finally, we proposed a method to solve the problem numerically and presented an application in medical imaging (Chapter 4). In the second part, we studied a nonlinear viscoelasticity system. We presented numerical methods to solve it and the implementation of these methods in three dimensions (Chapter 5). A biomedical application to the simulation of the brain shift was then considered (Chapter 6). Finally, we looked at some modelling issues by establishing a viscoelastic/viscoplastic model in large strains (Chapter 7).
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Contributor : Maya de Buhan <>
Submitted on : Wednesday, January 5, 2011 - 2:46:30 PM
Last modification on : Wednesday, December 9, 2020 - 3:11:07 PM
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  • HAL Id : tel-00552111, version 1

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Maya de Buhan. Problèmes inverses et simulations numériques en viscoélasticité 3D.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2010. Français. ⟨tel-00552111⟩

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