Artículo
An inverse problem in elastography involving Lamé systems
Autor/es | Fernández Cara, Enrique
Maestre Caballero, Faustino |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2018-02 |
Fecha de depósito | 2018-11-13 |
Publicado en |
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Resumen | This paper deals with some inverse problems for the linear elasticity system with origin in elastography: we try to identify the material coefficients from some extra information on (a part of) the boundary. In our main ... This paper deals with some inverse problems for the linear elasticity system with origin in elastography: we try to identify the material coefficients from some extra information on (a part of) the boundary. In our main result, we assume that the total variation of the coefficient matrix is a priori bounded. We reformulate the problem as the minimization of a function in an appropriate constraint set. We prove that this extremal problem possesses at least one solution with the help of some regularity results. Two crucial ingredients are a Meyers-like theorem that holds in the context of linear elasticity and a nonlinear interpolation result by Luc Tartar. We also perform some numerical experiments that provide satisfactory results. To this end, we apply the Augmented Lagrangian algorithm, completed with a limited-memory BFGS subalgorithm. Finally, on the basis of these experiments, we illustrate the influence of the starting guess and the errors in the data on the behavior of the iterates. |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | MTM2016-76990-P
MTM2014-53309-P |
Cita | Fernández Cara, E. y Maestre Caballero, F. (2018). An inverse problem in elastography involving Lamé systems. Journal of Inverse and Ill-posed Problems, 26 (5), 589-605. |
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