RCIN and OZwRCIN projects

Object

Title: On stability analysis in shape optimization: critical shapes for Neumann problem

Creator:

Żochowski, Antoni

Date issued/created:

2003

Resource type:

Tekst

Subtitle:

Raport Badawczy = Research Report ; RB/94/2003

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Description:

503-528 stron ; 21 cm ; Bibliografia s. 527-528

Abstract:

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 ifferentiability of the shape functional. In addition, it is shown that an appropriate regularization makes possible the stability of critical shapes.

Relation:

Raport Badawczy = Research Report

Detailed Resource Type:

Raport

Resource Identifier:

oai:rcin.org.pl:217409

Source:

RB-2003-94

Language:

eng

Language of abstract:

eng

Rights:

Licencja Creative Commons Uznanie autorstwa 4.0

Terms of use:

Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -

Digitizing institution:

Instytut Badań Systemowych Polskiej Akademii Nauk

Original in:

Biblioteka Instytutu Badań Systemowych PAN

Projects co-financed by:

Program Operacyjny Polska Cyfrowa, lata 2014-2020, Działanie 2.3 : Cyfrowa dostępność i użyteczność sektora publicznego; środki z Europejskiego Funduszu Rozwoju Regionalnego oraz współfinansowania krajowego z budżetu państwa

Access:

Otwarty

Object collections:

Last modified:

Oct 19, 2021

In our library since:

Oct 19, 2021

Number of object content downloads / hits:

21

All available object's versions:

https://rcin.org.pl./publication/255022

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