Naslov
On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus

Autori
Burazin, Krešimir

Izvornik
Journal of optimization theory and applications (0022-3239) 177 (2018), 2; 329-344

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Stationary diffusion ; Optimal design ; Homogenization ; Optimality conditions

Sažetak
We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA