| Abstract: |
| In this talk, I will discuss recent advances in solving elastic inverse problems, specifically focusing on the shape reconstruction of cavities and inclusions in a bounded linear isotropic medium using boundary measurements. Our approach leverages optimal control theory, reformulating the inverse problem as a minimization process. The objective is to minimize a misfit boundary functional or an energy-type functional, within the class of Lipschitz domains. To enhance the accuracy of the reconstruction, we introduce a regularization term that penalizes the perimeter of the cavity or inclusion being reconstructed. The optimization problem is tackled using a phase-field method, where the perimeter functional is approximated via the Modica-Mortola relaxation. |
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