Abstract: The identification problem of an inclusion is considered in the paper. The inclusion is unknown subdomain of a given physical region. The available information on the inclusion is governed by measurements on the boundary of this region. In particular, the single measurement problem of impedance electrotomography and similar inverse problems are included in our approach. The shape identification problem can be solved by the minimization of an objective function taking into account the measurement data. The best choice of such objective function is the Kohn-Vogelius energy functional. The standard regularization of the Kohn-Vogelius functional include the perimeter and Willmore curvature functional evaluated for an admissible inclusion boundary. In the two-dimensional case, a nonlocal existence theorem of strong solutions is proved for the gradient flow dynamical system generated for such a regularization of the Kohn-Vogelius functional. Bibliography: 24 titles.

Cite: Plotnikov P.I. , Sokolovskii Y.
GRADIENT FLOW FOR KOHN-VOGELIUS FUNCTIONAL
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2023. V.20. N1. P.524-579. DOI: 10.33048/semi.2023.20.032 WOS Scopus РИНЦ

Dates:

Submitted:	Mar 14, 2023
Accepted:	Jul 18, 2023

Identifiers:

Web of science:	WOS:001034303400003
Scopus:	2-s2.0-85167879549
Elibrary:	54768304

Citing:

DB	Citing
Elibrary	3
Scopus	1
Web of science	1

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