Abstract
In this paper, we are interested in the numerical shape recognition. This work takes into account some theoretical results already established the paper published by Ndiaye et al. (Bull Math Anal Appl 4(1):91–103, 2012) and provides additional tools of shape optimization under constraints described by non linear parabolic PDE. We propose also algorithms and numerical methods to recognize an unattainable part of a bounded domain in which an elliptic linear boundary value problem is satisfied.
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Notes
- 1.
The software FreeFem++ software, developed at UPMC by F. Hecht and O. Pironneau, is a high-level integrated developing environment for solving (system of) partial differential equations in two and three dimensions of space.
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Sadio, G.I., Seck, A., Seck, D. (2022). Numerical and Theoretical Analysis for Optimal Shape Inverse Problems. In: Seck, D., Kangni, K., Nang, P., Salomon Sambou, M. (eds) Nonlinear Analysis, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-04616-2_12
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