Gradient Flows in Shape Optimization Theory

Gradient Flows in Shape Optimization Theory Full article

Journal

Doklady Mathematics
ISSN: 1064-5624

Output data

Year: 2023, Number: 108, Pages: 387–391 Pages count : 5 DOI: 10.1134/s1064562423700990

Tags

shape optimization, inverse problems, Willmore flow, Euler elastica

Authors

П. И. Плотников ¹ , Jan Sokołowski ^2,3,4

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2	Department of Scientific Computing, Informatics Center, Federal University of Paraiba, Joao Pessoa, Brazil
3	Institut Elie Cartan, Laboratoire de Mathematiques, Universite de Lorraine, Nancy, France
4	Systems Research Institute of Polish Academy of Sciences, Warszawa, Poland

The problem of identifying an inclusion is considered. The inclusion is an unknown subdomain of a given physical region. Available information on the inclusion is given by measurements on the boundary of this region. This class of problems includes single-measurement electrical impedance tomography and other inverse problems. The shape identification problem can be solved by minimizing an objective function characterizing the deviation of a given configuration from an admissible solution of the problem. The best choice of such an objective function is the Kohn–Vogelius energy functional. The standard regularization of the Kohn–Vogelius functional is considered, which is obtained by adding to the functional a linear combination of the perimeter of the inclusion and the Willmore curvature functional evaluated for an admissible inclusion boundary. In the two-dimensional case, a nonlocal theorem on the existence of strong solutions is proved for the gradient flow dynamical system generated for such a regularization of the Kohn–Vogelius functional

П. И. Плотников , Jan Sokołowski
Gradient Flows in Shape Optimization Theory
Doklady Mathematics. 2023. N108. P.387–391. DOI: 10.1134/s1064562423700990 WOS Scopus РИНЦ OpenAlex

Submitted:	Feb 6, 2023
Accepted:	Aug 7, 2023
Published print:	Oct 30, 2023

Web of science:	WOS:001097713700001
Scopus:	2-s2.0-85175267653
Elibrary:	63935826
OpenAlex:	W4388021830

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Elibrary	1
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