Author:
Abdelwahed Mohamed,Chorfi Nejmeddine,Hassine Maatoug
Abstract
AbstractWe study the determination of some rigid inclusions immersed in an isotropic elastic medium from overdetermined boundary data. We propose an accurate approach based on the topological sensitivity technique and the reciprocity gap concept. We derive a higher-order asymptotic formula, connecting the known boundary data and the unknown inclusion parameters. The obtained formula is interesting and useful tool for developing accurate and robust numerical algorithms in geometric inverse problems.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference20 articles.
1. Pasquale, C., Leszek, G., Roberto, L., Junior Joao, S.: Multiplicity of positive solutions for a degenerate nonlocal problem with p-laplacian. Adv. Nonlinear Anal. 11(1), 357–368 (2022)
2. Blatt, S., Hopper, C., Vorderobermeier, N.: A regularized gradient flow for the p-elastic energy. Adv. Nonlinear Anal. 11, 1383–1411 (2022)
3. Muvasharkhan, J., Murat, R., Madi, Y.: On the numerical solution of one inverse problem for a linearized two-dimensional system of navier-stokes equations. Opusc. Math. 42(5), 709–725 (2022)
4. Garcke, H., Huttl, P., Knopf, P.: Shape and topology optimization involving the eigenvalues of an elastic structure: a multi-phase-field approach. Adv. Nonlinear Anal. 11, 159–197 (2022)
5. Abdelwahed, M., Chorfi, N., Hassine, M.: Asymptotic formulas for the identification of small inhonogeneities in a fluid midium. Electron. J. Differ. Equ. 186, 1 (2015)