Inverse problems for elastic body with delaminated volume inclusion

Inverse problems for elastic body with delaminated volume inclusion Full article

Journal

Zeitschrift fur Angewandte Mathematik und Physik
ISSN: 0044-2275

Output data

Year: 2026, Volume: 77, Number: 8, Article number : 77:243, Pages count : 15 DOI: 10.1007/s00033-026-02891-w

Tags

Solution existence, Non-coercivity, Neumann boundary conditions, Non-penetration boundary conditions, Inverse problem

Authors

Khludnev Alexander ¹

Affiliations

1	Lavrentyev Institute of Hydrodynamics of RAS, Novosibirsk, 630090, Russia

The paper investigates an equilibrium problem for an elastic body with a volume inclusion assuming that the inclusion is delaminated from the surrounding material thus forming an interfacial crack. Neumann type boundary conditions imposed on external boundary of the body provide a non-coercivity of the problem. Moreover, non-linear boundary conditions are considered at the crack faces which implies a mutual non-penetration between them. Thus, the direct problem under consideration belongs to the class of problems with unknown contact set. Necessary and sufficient conditions imposed on external forces are found for a solvability of the direct problem. Assuming that there is an additional information concerning the solution we analyze various inverse problems. In this case, an additional information concerning the solution is provided. This information can be obtained using measurements. An existence and uniqueness of solutions is analyzed for all cases.

Khludnev A.
Inverse problems for elastic body with delaminated volume inclusion
Zeitschrift fur Angewandte Mathematik und Physik. 2026. V.77. N8. 77:243 :1-15. DOI: 10.1007/s00033-026-02891-w WOS Scopus OpenAlex

Submitted:	May 13, 2026
Accepted:	Jul 29, 2026
Published print:	Aug 12, 2026

≡ Web of science:	WOS:001848503800002
≡ Scopus:	2-s2.0-105047017957
≡ OpenAlex:	W7202247194