Geodesic
Optimal location problem for composite bodies with separate and joined rigid inclusions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 19-30

Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear mathematical models describing an equilibrium state of composite bodies which may come into contact with a fixed non-deformable obstacle are investigated. We suppose that the composite bodies consist of an elastic matrix and one or two built-in volume (bulk) rigid inclusions. These inclusions have a rectangular shape and one of them can vary its location along a straight line. Considering a location parameter as a control parameter, we formulate an optimal control problem with a cost functional specified by an arbitrary continuous functional on the solution space. Assuming that the location parameter varies in a given closed interval, the solvability of the optimal control problem is established. Furthermore, it is shown that the equilibrium problem for the composite body with joined two inclusions can be considered as a limiting problem for the family of equilibrium problems for bodies with two separate inclusions.
Keywords: optimal control problem, composite body, Signorini conditions, rigid inclusion, location. 
@article{IIGUM_2023_43_a1,
     author = {Nyurgun P. Lazarev and Galina M. Semenova},
     title = {Optimal location problem for composite bodies with separate and joined rigid inclusions},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {19--30},
     publisher = {mathdoc},
     volume = {43},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a1/}
}
TY  - JOUR
AU  - Nyurgun P. Lazarev
AU  - Galina M. Semenova
TI  - Optimal location problem for composite bodies with separate and joined rigid inclusions
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2023
SP  - 19
EP  - 30
VL  - 43
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a1/
LA  - en
ID  - IIGUM_2023_43_a1
ER  - 
%0 Journal Article
%A Nyurgun P. Lazarev
%A Galina M. Semenova
%T Optimal location problem for composite bodies with separate and joined rigid inclusions
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2023
%P 19-30
%V 43
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a1/
%G en
%F IIGUM_2023_43_a1
Nyurgun P. Lazarev; Galina M. Semenova. Optimal location problem for composite bodies with separate and joined rigid inclusions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 19-30. http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a1/