- Tytuł:
- On stability analysis in shape optimisation : critical shapes for Neumann problem
- Autorzy:
-
Dambrine, M.
Sokolowski, J.
Żochowski, A. - Powiązania:
- https://bibliotekanauki.pl/articles/970525.pdf
- Data publikacji:
- 2003
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
optymalizacja kształtu
analiza stabilności
gradient kształtu
shape optimisation
stability analysis
shape gradient
shape Hessian - Opis:
- The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then, the new estimates for the shape Hessian are derived in order to overcome the classical two norms-discrepancy well know in control problems, Malanowski (2001). In the context of shape optimization, the situation is similar compared to control problems, actually, the shape Hessian can be coercive only in the norm strictly weaker with respect to the norm of the second order differentiability of the shape functional. In addition, it is shown that an appropriate regularization makes possible the stability of critical shapes.
- Źródło:
-
Control and Cybernetics; 2003, 32, 3; 503-528
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł